1 Introduction 1
2 Expository books on mathematics and mathematicians 5
2.1 Popular and expository books on mathematics 6
2.1.1 R.Courant,H.Robbins,What Is Mathematics? Oxford University Press,New York,1941.xix+521 pp 6
2.1.2 A.D.Aleksandrov,A.N.Kolmogorov,M.A.Lavrent'ev,Mathemat-ics:Its Content,Methods,and Meaning.Vol.Ⅰ,Vol.Ⅱ,Vol.Ⅲ,The M.I.T.Press,Cambridge,Mass.,1963,xi+359 pp.;xi+377 pp.;xi+356 pp..Translated by S.H.Gould and T.Bartha;S.H.Gould;K.Hirsch 12
2.1.3 G.Pólya,How to Solve it.A New Aspect of Mathematical Method.Expanded version of the 1988 edition,with a new foreword by John H.Conway,Princeton Science Library,Princeton University Press,2004.xxviii+253 pp 15
2.1.4 G.H.Hardy,A Mathematician's Apology,With a foreword by C.P.Snow,Reprint of the 1967 edition,Canto,Cambridge University Press,Cambridge,1992 19
2.1.5 J.E.Littlewood,Littlewood's Miscellany,Edited and with a fore-word by Bola Bollobas,Cambridge University Press,Cambridge,1986.vi+200 pp 21
2.1.6 Autobiographies of mathematicians 22
2.1.7 H.Weyl,Symmetry.Reprint of the 1952 original.Princeton Sci-ence Library.Princeton University Press,Princeton,N.J.,1989 27
2.1.8 D.Hilbert,S.Cohn-Vossen,Geometry and the Imagination,Amer-ican Mathematical Society,1,1999.35 7 pages 37
2.2 Biographies of mathematicians and history of mathematics 42
2.2.1 E.T.Bell,Men of Mathematics,Touchstone,1986.6 08 pages 42
2.2.2 C.Reid,Hilbert,Springer-Verlag,New York-Berlin,1970.xi+290 pp 44
2.2.3 More biographies of mathematicians 46
2.2.4 A.Weil,Number Theory.An Approach through History.From Hammurapi to Legendre.Birkh？user Boston,MA,1984.xxi+375 pp 55
2.2.5 W.Scharlau,H.Opolka,From Fermat to Minkowski.Lectures on the Theory of Numbers and its Historical Development,Under-graduate Texts in Mathematics.Springer-Verlag,New York,1985.xi+184 pp 58
2.2.6 History of mathematics 59
2.2.7 More mathematical history books 62
2.2.8 J.Dieudonné,A History of Algebraic and Differential Topology 1900-1960,Reprint of the 1989 edition,Modern Birkh？user Clas-sics.Birkh？user Boston,Inc.,Boston,MA,2009.xxii+648 pp 72
2.2.9 History of Lie groups and related spaces 73
2.2.10 F.Klein,Development of Mathematics in the 19th Century,With a preface and appendices by Robert Hermann,Translated from the German by M.Ackerman.Math Sci Press,Brookline,Mass.,1979.ix+630 pp 75
3 Analysis 79
3.1 Calculus and real analysis 79
3.1.1 G.H.Hardy,A Course of Pure Mathematics,Reprint of the(1952) tenth edition,Cambridge Mathematical Library,Cambridge Uni-versity Press,Cambridge,1992.xii+509 pp 80
3.1.2 Calculus 82
3.1.3 E.T.Whittaker and G.N.Watson,A Course of Modern Analysis,An Introduction to the General Theory of Infinite Processes and of Analytic Functions:with an Account of the Principal Transcen-dental Functions,Fourth edition.Reprinted,Cambridge University Press,New York,1962,vii+608 pp 85
3.1.4 Special functions 85
3.1.5 W.Rudin,Real and Complex Analysis,Third edition,McGraw-Hill Book Co.,New York,1987.xiv+416 pp 90
3.1.6 More books on real analysis 90
3.1.7 Measure theory 97
3.1.8 Analysis on general spaces 100
3.1.9 G.Pólya,G.Szeg？,Problems and Theorems in Analysis.Vol.Ⅰ.Series,Integral calculus,Theory of Functions.Vol.Ⅱ.Theory of Functions,Zeros,Polynomials,Determinants,Number Theory,Geometry,Grundlehren der mathematischen Wissenschaften,Clas-sics in Mathematics,Springer-Verlag,Berlin,1998.xii+392 pp.xx+389 pp 104
3.1.10 Orthogonal polynomials 106
3.1.11 Problem books 107
3.1.12 G.H.Hardy,J.E.Littlewood,G.Pólya,Inequalities,Reprint of the 1952 edition,Cambridge Mathematical Library,Cambridge Uni-versity Press,Cambridge,1988.xii+324 pp 110
3.2 Complex analysis 114
3.2.1 H.Cartan,Elementary Theory of Analytic Functions of One or Several Complex Variables. ？ditions Scientifiques Hermann,Paris;Addison-Wesley Publishing Co.,Inc.,Reading,Mass.-Palo Alto,Calif.-London,1963.22 8 pp 115
3.2.2 L.Ahlfors,Complex Analysis,Third edition,International Series in Pure and Applied Mathematics,McGraw-Hill Book Co.,New York,1978.xi+331 pp 115
3.2.3 R.Remmert,Theory of Complex Functions,Translated from the second German edition by Robert B.Burckel,Graduate Texts in Mathematics,122,Readings in Mathematics,Springer-Verlag,New York,1991.xx+453 pp 116
3.2.4 More books on complex analysis 117
3.2.5 Analytic and meromorphic functions,and conformal maps 121
3.2.6 Several complex variables 123
3.2.7 Sheaf theories 126
3.2.8 H.Weyl,The Concept of a Riemann Surface,Translated from the third German edition by Gerald R.MacLane,ADIWES Interna-tional Series in Mathematics,Addison-Wesley Publishing Co.,Inc.,Reading,Mass.-London,1964.xi+191 pp 128
3.2.9 More books on Riemann surfaces 130
3.2.10 Quasiconformal mappings 132
3.2.11 Teichmüller theory 135
3.3 Harmonic analysis 140
3.3.1 Y.Katznelson,An Introduction to Harmonic Analysis,3rd Edition,Cambridge Mathematical Library,Cambridge University Press,2004.xviii+314 pp 141
3.3.2 More books on harmonic analysis and Fourier series 142
3.3.3 A.Zygmund,Trigonometric Series.2 nd ed.Vols.Ⅰ,Ⅱ.Cambridge University Press,New York,1959,Vol.Ⅰ.,xii+383 pp.;Vol.Ⅱ.vii+354 pp 147
3.3.4 Potential theory 149
3.3.5 J.Garnett,Bounded Analytic Functions,Pure and Applied Math-ematics,96,Academic Press,Inc.,New York-London,1981.xvi+467 pp 152
3.3.6 More books on Hardy spaces and function spaces 153
3.3.7 E.Stein,Singular Integrals and Differentiability Properties of Func-tions,Princeton Mathematical Series,No.30 ,Princeton University Press,1970,xiv+290 pp 157
3.3.8 G.Folland,Harmonic Analysis in Phase Space,Annals of Math-ematics Studies,122,Princeton University Press,Princeton,N.J.,1989.x+277 pp 160
3.3.9 I.Daubechies,Ten Lectures on Wavelets,CBMS-NSF Regional Conference Series in Applied Mathematics,61,Society for Indus-trial and Applied Mathematics(SIAM),Philadelphia,PA,1992.xx+357 pp 160
3.4 Functional analysis and operator theory 162
3.4.1 S.Banach,Theory of Linear Operations,Translated from the French by F.Jellett,With comments by A.Peczyski and Cz.Bessaga,North-Holland Mathematical Library,38,North-Holland Publish-ing Co.,Amsterdam,1987.x+237 pp 163
3.4.2 More basic books on functional analysis 164
3.4.3 More books on Banach spaces 167
3.4.4 More books on Hilbert spaces 169
3.4.5 L.Schwartz,Théorie des Distributions,Hermann,Paris,1966,xiii+420 pp 171
3.4.6 I.M.Gel'fand,G.E.Shilov,Generalized Functions.Vol.1.Prop-erties and Operations,Vol.2.Spaces of Fundamental and Gen-eralized Functions,Vol.3.Theory of Differential Equations,I.M.Gel'fand,N.Ya.Vilenkin,Vol.4.Applications of Harmonic Anal-ysis,I.M.Gel'fand,M.I.Graev,N.Ya.Vilenkin,Vol.5.Integral Geometry and Representation Theory,Academic Press,New York-London,1964,xviii+423 pp.,x+261 pp.,x+222 pp.,xiv+384 pp.,xvii+449 pp 172
3.4.7 K.Yosida,Functional analysis,reprint of the sixth(1980)edition.Classics in Mathematics,Springer-Verlag,Berlin,1995.xii+501 pp 174
3.4.8 N.Dunford,J.Schwartz,Linear Operators,Part Ⅰ,General The-ory;Part Ⅱ,Spectral theory.Selfadjoint operators in Hilbert space.Part Ⅲ,Spectral operators,Wiley Classics Library,A Wiley-Interscience Publication,John Wiley ＆ Sons,Inc.,New York,1988.xiv+858 pp.,x+859-1923,xx+1925-2592 175
3.4.9 Semigroups and functional analysis 176
3.4.10 A.Connes,Noncommutative Geometry,Academic Press,Inc.,San Diego,CA,1994.xiv+661 pp 178
3.4.11 Operator algebras 179
3.4.12 H.Brezis,Analyse Fonctionnelle,Théorie et Applications,Collec-tion Mathématiques Appliquées pour la Matrise.Masson,Paris,1983.xiv+234 pp 184
3.4.13 K.Deimling,Nonlinear Functional Analysis,Springer-Verlag,Berlin,1985.xiv+450 pp 185
4 Algebra 187
4.1 Abstract algebras and finite groups 188
4.1.1 Linear algebra 188
4.1.2 Advanced linear algebra and matrix algebra 191
4.1.3 van der Waerden,Algebra.Vol.Ⅰ.,Algebra.Vol.Ⅱ.,Based in part on lectures by E.Artin and E.Noether,Translated from the fifth German edition by John R.Schulenberge,Springer-Verlag,New York,1991.xiv+265 pp.,xii+284 pp 194
4.1.4 More books on abstract algebra 196
4.1.5 I.R.Shafarevich,Basic Notions of Algebra,Springer,Berlin,1990;Springer-Verlag,Berlin,1997.iv+258 pp 204
4.1.6 R.Carter,Simple Groups of Lie Type,Pure and Applied Math-ematics,Vol.28 ,Reprint of the 1972 original,Wiley Classics Li-brary,A Wiley-Interscience Publication,John Wiley ＆ Sons,Inc.,New York,1989.x+335 pp 205
4.1.7 Finite groups 206
4.1.8 Finite groups and their representation theories 213
4.1.9 Representation theories and associate algebras 214
4.1.10 Rings and modules 216
4.2 Commutative algebras 218
4.3 Homological algebra 225
4.3.1 H.Cartan,S.Eilenberg,Homological Algebra,With an appendix by David A.Buchsbaum,Reprint of the 1956 original,Princeton Landmarks in Mathematics,Princeton University Press,Princeton,NJ,1999.xvi+390 pp 226
4.3.2 More books on homological algebra and related subjects 228
5 Geometry 233
5.1 Differential geometry 233
5.1.1 H.Hopf,Differential Geometry in the Large,Notes taken by Peter Lax and John Gray,With a preface by S.S.Chern,Lecture Notes in Mathematics,1000,Springer-Verlag,Berlin,1983.vii+184 pp 234
5.1.2 Introduction to differential geometry and Riemannian geometry 235
5.1.3 More advanced books on Riemannian geometry 240
5.1.4 Special topics in differential geometry 245
5.1.5 M.Gromov,Metric Structures for Riemannian and Non-Riemannian Spaces,Based on the 1981 French original,With appendices by M.Katz,P.Pansu and S.Semmes,Translated from the French by Sean Michael Bates,Progress in Mathematics,152,Birkh？user Boston,Inc.,Boston,MA,1999.xx+585 pp 253
5.1.6 M.Bridson,A.Haefliger,Metric Spaces of Non-positive Curvature,Grundlehren der Mathematischen Wissenschaften,319,Springer-Verlag,Berlin,1999.xxii+643 pp 255
5.1.7 S.Helgason,Differential Geometry,Lie Groups,and Symmetric Spaces,Corrected reprint of the 1978 original,Graduate Studies in Mathematics,34,American Mathematical Society,Providence,RI,2001.xxvi+641 pp 256
5.2 Geometric analysis 258
5.2.1 R.Schoen,S.T.Yau,Lectures on Differential Geometry,Interna-tional Press,1994.v+235 pp 259
5.2.2 T.Aubin,Nonlinear Analysis on Manifolds,Monge Ampére equa-tions,Grundlehren der Mathematischen Wissenschaften,252,Springer-Verlag,New York,1982.xii+204 pp 260
5.2.3 More books on geometric analysis 260
5.2.4 M.Gromov,Partial Differential Relations,Ergebnisse der Mathe-matik und ihrer Grenzgebiete(3),9,Springer-Verlag,Berlin,1986.x+363 pp 264
5.2.5 H.Federer,Geometric Measure Theory,Die Grundlehren der math-ematischen Wissenschaften,Band 153,Springer-Verlag New York Inc.,New York,1969,xiv+676 pp 265
5.2.6 More books on geometric measure theory 266
5.2.7 Calculus of variation 267
5.2.8 Fractal geometry 270
5.3 Complex geometry and complex analysis 272
5.3.1 L.H？rmander,An Introduction to Complex Analysis in Several Variables,Third edition,North-Holland Publishing Co.,Amster-dam,1990.xii+254 pp 272
5.3.2 More books on complex geometry 273
5.3.3 C.L.Siegel,Topics in Complex Function Theory.Vol.Ⅰ.Elliptic Functions and Uniformization Theory.Vol.Ⅱ.Automorphic Func-tions and Abelian Integrals.Vol.Ⅲ.Abelian Functions and Mod-ular Functions of Several Variables,Interscience Tracts in Pure and Applied Mathematics,No.25 ,Wiley-Interscience,1969.ix+186 pp.,1988.xii+193 pp.,1989.x+244 pp 276
5.4 Algebraic geometry 277
5.4.1 A.Grothendieck,The ？léments de géométrie algébrique,Inst.Hautes ？tudes Sci.Publ.Math.,1960-1967 279
5.4.2 I.Shafarevich,Basic Algebraic Geometry.1.Varieties in Projec-tive Space.2.Schemes and Complex Manifolds.Second edition,Springer-Verlag,Berlin,1994.xx+303 pp.,xiv+269 pp 281
5.4.3 D.Mumford,The Red book of Varieties and Schemes,Second,ex-panded edition.Includes the Michigan lectures(1974) on curves and their Jacobians,With contributions by Enrico Arbarello.Lec-ture Notes in Mathematics,1358.Springer-Verlag,Berlin,1999.x+306 pp 283
5.4.4 R.Hartshorne,Algebraic Geometry,Graduate Texts in Mathemat-ics,No.5 2,Springer-Verlag,New York-Heidelberg,1977.xvi+496 pp 285
5.4.5 P.Griffiths,J.Harris,Principles of Algebraic Geometry,Pure and Applied Mathematics,Wiley-Interscience,New York,1978.xii+813 pp 286
5.4.6 Introduction to algebraic geometry and algebraic curves 288
5.4.7 Topology of algebraic varieties 289
5.4.8 Symplectic geometry and symplectic topology 290
5.4.9 D.Mumford,J.Fogarty,F.Kirwan,Geometric invariant theory,Third edition,Ergebnisse der Mathematik und ihrer Grenzgebiete(2),34,Springer-Verlag,Berlin,1994.xiv+292 pp 293
5.4.10 Classification of varieties and moduli spaces 294
5.4.11 Algebraic curves 297
5.4.12 Algebraic surfaces 299
5.4.13 W.Fulton,Intersection Theory,Second edition,Ergebnisse der Mathematik und ihrer Grenzgebiete.3.Folge,Springer-Verlag,Berlin,1998.xiv+470 pp 302
5.4.14 R.Lazarsfeld,Positivity in Algebraic Geometry.Ⅰ.Classical Set-ting:Line Bundles and Linear Series;Ⅱ.Positivity for Vector Bun-dles,and Multiplier Ideals,Ergebnisse der Mathematik und ihrer Grenzgebiete.3.Folge,Springer-Verlag,Berlin,2004.xviii+387 pp.,xviii+385 pp 305
5.4.15 Toric varieties 306
5.5 Convex geometry and discrete geometry 309
5.5.1 R.T.Rockafellar,Convex Analysis,Princeton Mathematical Se-ries,No.28 ,Princeton University Press,Princeton,N.J.,1970.xviii+451 pp 309
5.5.2 Convex functions and convex geometry 311
6 Topology 315
6.1 More classical topology 316
6.1.1 P.Alexandroff,H.Hopf,Topologie I.Berlin,Springer,1935.xiii+636 pp 316
6.1.2 K.Kuratowski,Topology.Vol.Ⅰ.,Vol.Ⅱ.,New edition,Revised and augmented,Translated from the French by J.Jaworowski Aca-demic Press,New York-London;Pa？stwowe Wydawnictwo Naukowe,Warsaw,1966.xx+560 pp.,1968.xiv+608 pp 318
6.1.3 More books on topology 318
6.1.4 Fixed point theory 321
6.1.5 Dimension theory 322
6.2 Algebraic topology 324
6.2.1 J.Milnor,J.Stasheff,Characteristic Classes,Annals of Mathe-matics Studies,No.7 6,Princeton University Press,1974.vii+331 pp 324
6.2.2 S.Eilenberg,N.Steenrod,Foundations of Algebraic Topology,Prince-University Press,1952.xv+328 pp 326
6.2.3 More books on algebraic topology 326
6.2.4 D.Rolfsen,Knots and Links,Corrected reprint of the 1976 original,Mathematics Lecture Series,7,Publish or Perish,Inc.,Houston,TX,1990.xiv+439 pp 329
6.2.5 More knots and their invariants books 330
6.3 Generalized cohomology theory and homotopy theories 332
6.3.1 J.Adams,Stable Homotopy and Generalised Homology,Chicago Lectures in Mathematics,University of Chicago Press,Chicago,Ill.-London,1974.x+373 pp 332
6.3.2 K-theory 333
6.3.3 K.Brown,Cohomology of Groups,Graduate Texts in Mathemat-ics,87,Corrected reprint of the 1982 original,Graduate Texts in Mathematics,87,Springer-Verlag,New York,1994.x+306 pp 335
6.3.4 G.W.Whitehead,Elements of Homotopy Theory,Graduate Texts in Mathematics,61,Springer-Verlag,New York-Berlin,1978.xxi+744 pp 337
6.4 Differential topology 338
6.4.1 J.Milnor,Morse Theory,Based on lecture notes by M.Spivak and R.Wells,Annals of Mathematics Studies,No.5 1,Princeton University Press,Princeton,N.J.,1963.vi+153 pp 339
6.4.2 Differential topology 340
6.4.3 R.Bott,L.Tu,Differential Forms in Algebraic Topology,Graduate Texts in Mathematics,82,Springer-Verlag,New York-Berlin,1982.xiv+331 pp 341
6.4.4 W.V.D.Hodge,The Theory and Applications of Harmonic Inte-grals,Reprint of the 1941 original,With a foreword by Michael Atiyah,Cambridge Mathematical Library,Cambridge University Press,Cambridge,1989.xiv+284 pp 342
6.4.5 M.Goresky,R.MacPherson,Stratified Morse theory,Ergebnisseder Mathematik und ihrer Grenzgebiete(3),14,Springer-Verlag,Berlin,1988.xiv+272 pp 343
6.5 Geometric topology 345
6.5.1 W.Thurston,The Geometry and Topology of Three-Manifolds,Lecture notes at Princeton University,1978-1980 345
6.5.2 Four dimensional manifolds 350
6.5.3 Geometric topology and surgery theory 351
7 Number theory 355
7.1 Number theory 356
7.1.1 G.H.Hardy,E.Wright,An Introduction to the Theory of Numbers,Sixth edition,Revised by D.R.Heath-Brown and J.H.Silverman,With a foreword by Andrew Wiles,Oxford University Press,Ox-ford,2008.xxii+621 pp 356
7.1.2 Books on basic number theory 357
7.1.3 H.Davenport.The Higher Arithmetic.An Introduction to the The-ory of Numbers,Eighth edition,With editing and additional ma-terial by James H.Davenport,Cambridge University Press,Cam-bridge,2008.x+239 pp 361
7.1.4 H.Hasse,Number Theory,Translated from the third German edi-tion and with a preface by Horst Günter Zimmer.Grundlehre nder Mathematischen Wissenschaften,229.Springer-Verlag,Berlin-New York,1980.xvii+638 pp 362
7.1.5 A.Borevich,I.Shafarevich,Number Theory,Translated from the Russian by Newcomb Greenleaf,Pure and Applied Mathematics,Vol.20 ,Academic Press,New York-London,1966,x+435 pp 362
7.1.6 A.Y.Khinchin,Three Pearls of Number Theory,Translated from the Russian by F.Bagemihl,H.Komm,and W.Seidel,Reprint of the 1952 translation,Dover Publications,Inc.,Mineola,NY,1998.6 4 pp 363
7.1.7 E.Artin,Galois Theory,Notre Dame Mathematical Lectures,No.2 ,Edited and with a supplemental chapter by Arthur N.Milgram,Reprint of the 1944 second edition,Dover Publications,Inc.,Mi-neola,N.Y.,1998.iv+82 pp 364
7.2 Algebraic number theory 365
7.2.1 D.Hilbert,The Theory of Algebraic Number Fields,Translated from the German and with a preface by Iain T.Adamson,With an introduction by Franz Lemmermeyer and Norbert Schappacher,Springer-Verlag,Berlin,1998.xxxvi+350 pp 365
7.2.2 E.Hecke,Lectures on the Theory of Algebraic Numbers,Trans-lated from the German by George U.Brauer,Jay R.Goldman and R.Kotzen,Graduate Texts in Mathematics,77,Springer-Verlag,New York-Berlin,1981.xii+239 pp 366
7.2.3 J.W.S.Cassels,A.Fr？hlich,Algebraic Number Theory,Proceed-ings of the instructional conference held at the University of Sus-sex,Brighton,September 1-17,1965,Academic Press,London;Thompson Book Co.,Inc.,Washington,D.C.,1967,xviii+366 pp 367
7.2.4 S.Lang,Algebraic Number Theory,Second edition,Graduate Texts in Mathematics,110,Springer-Verlag,New York,1994.xiv+357 pp 368
7.2.5 More books on algebraic number theory 368
7.2.6 Computational algebraic number theory 370
7.2.7 J.P.Serre.Local Fields.Translated from the French by Marvin Jay Greenberg,Graduate Texts in Mathematics,67,Springer-Verlag,New York-Berlin,1979.viii+241 pp 371
7.2.8 Galois cohomology 372
7.2.9 Geometry of numbers 373
7.3 Analytic number theory 374
7.3.1 E.C.Titchmarsh,The Theory of the Riemann Zeta-Function,Sec-ond edition.Edited and with a preface by D.R.Heath-Brown,The Clarendon Press,Oxford University Press,New York,1986.x+412 pp 375
7.3.2 More books on the Riemann zeta function 375
7.3.3 Analytic number theory 377
7.3.4 Additive number theory 380
7.3.5 Multiplicative number theory 381
7.4 Transcendental number theory 382
7.5 Arithmetic algebraic geometry 384
7.5.1 G.Shimura,Introduction to the Arithmetic Theory of Automor-phic Functions,Iwanami Shoten,Publishers,Tokyo;Princeton Uni-versity Press,Princeton,N.J.,1971.xiv+267 pp 384
7.5.2 J.P.Serre,A Course in Arithmetic,Translated from the French,Graduate Texts in Mathematics,No.7 ,Springer-Verlag,New York-Heidelberg,1973.viii+115 pp 385
7.5.3 J.Silverman,The Arithmetic of Elliptic Curves,Graduate Texts in Mathematics,106,Second edition,Graduate Texts in Mathe-matics,106,Springer,Dordrecht,2009.xx+513 pp 385
7.5.4 D.Mumford,Abelian Varieties.With appendices by C.P.Ra-manujam and Yuri Manin,Corrected reprint of the second(1974)edition,Tata Institute of Fundamental Research Studies in Math-ematics,5,Hindustan Book Agency,New Delhi,2008.xii+263 pp 387
7.5.5 Abalian varieties and theta functions 387
7.5.6 Diophantine geometry 389
7.5.7 Etale cohomology 390
7.5.8 Quadratic forms 391
7.5.9 More books on number theory 393
7.6 Modular forms and automorphic representations 395
7.6.1 R.Fricke,F.Klein,Vorlesungen uber die Theorie der automorphen Funktionen.Band 1:Die gruppentheoretischen Grundlagen.Band Ⅱ:Die funktionentheoretischen Ausfhrungen und die Andwendun-gen. Bibliotheca Mathematica Teubneriana,Bande 3,4,John-son Reprint Corp.,New York;B.G.Teubner Verlagsgesellschaft,Stuttg art 1965.Band Ⅰ:xiv+634 pp.:Band Ⅱ: xiv+668 pp 396
7.6.2 I.M.Gel'fand,M.Graev,I.I.Pyatetskii-Shapiro,Representation Theory and Automorphic Functions,W.B.Saunders Co.,Philadel-phia,Pa.-London-Toronto,Ont.19 69.xvi+426 pp 399
7.6.3 H.Jacquet,R.Langlands,Automorphic Forms on GL(2),Lecture Notes in Mathematics,Vol.11 4,Springer-Verlag,Berlin-New York,1970.vii+548 pp 400
7.6.4 More books on modular forms and automorphic forms 401
7.6.5 R.Langlands,On the Functional Equations Satisfied by Eisenstein Series,Lecture Notes in Mathematics,Vol.5 44,Springer-Verlag,Berlin-New York,1976.v+337 pp 402
7.6.6 A.Borel,W.Casselman,Automorphic Forms,Representations and L-functions.Part 1,Part 2,Proceedings of Symposia in Pure Mathematics,ⅩⅩⅩⅢ.American Mathematical Society,Providence,R.I.,1979.x+322 pp.,vii+382 pp 403
7.6.7 More books on modular forms,automorphic representations and cohomology of arithmetic groups 404
7.6.8 Hypergeometric series and theory of partitions 405
8 Differential equations 407
8.1 Ordinary differential equations 407
8.1.1 E.Coddington,N.Levinson,Theory of Ordinary Differential Equa-tions,McGraw-Hill Book Company,Inc.,New York-Toronto-London,1955.xii+429 pp 408
8.1.2 More books on ordinary differential equations 409
8.1.3 V.I.Arnold,Ordinary Differential Equations,Translated from the third Russian edition by Roger Cooke,Springer Textbook,Springer-Verlag,Berlin,1992.33 4 pp 410
8.1.4 More books on ordinary differential equations and dynamical systems 411
8.2 Linear differential operators 413
8.2.1 L.Evans,Partial Differential Equations,Graduate Studies in Math-ematics,19,Second edition,Graduate Studies in Mathematics,19,American Mathematical Society,Providence,RI,2010.xxii+749 pp 413
8.2.2 L.H？rmander,Linear Partial Differential Operators,Springer Ver-lag,Berlin-New York,1976.vii+285 pp 414
8.2.3 More books on linear differential equations 416
8.2.4 Inverse problems 418
8.2.5 Critical point theory and minimax methods 419
8.2.6 D.Gilbarg,N.Trudinger,Elliptic Partial Differential Equations of Second Order,Reprint of the 1998 edition,Classics in Mathematics,Springer-Verlag,Berlin,2001.xiv+517 pp 421
8.2.7 More books on elliptic differential equations 421
8.2.8 Pseudodifferential operators 423
8.2.9 Parabolic equations 425
8.2.10 R.Adams,John J.H.Fournier,Sobolev Spaces,Second edition,Pure and Applied Mathematics(Amsterdam),140,Elsevier/Academic Press,Amsterdam,2003.xiv+305 pp 427
8.2.11 More books on Sobolev spaces 427
8.2.12 T.Kato,Perturbation Theory for Linear Operators,Reprint of the 1980 edition,Classics in Mathematics,Springer-Verlag,Berlin,1995 428
8.3 Nonlinear differential equations 429
8.3.1 More geometric nonlinear differential equations 429
8.3.2 Nonlinear differential equations and fluid mechanics 432
9 Lie theories 439
9.1 Lie groups and Lie algebras 440
9.1.1 C.Chevalley,Theory of Lie Groups.I,Fifteenth printing,Prince-ton Mathematical Series,8,Princeton Landmarks in Mathematics,Princeton University Press,Princeton,NJ,1999.xii+217 pp 440
9.1.2 J.P.Serre,Complex Semisimple Lie Algebras,Translated from the French by G.A.Jones,Reprint of the 1987 edition,Springer Mono-graphs in Mathematics,Springer-Verlag,Berlin,2001.x+74 pp 441
9.1.3 N.Bourbaki,Lie Groups and Lie Algebras.Chapters 4-6,Trans-lated from the 1968 French original by Andrew Pressley.Elements of Mathematics(Berlin),Springer-Verlag,Berlin,2002.xii+300 pp 442
9.1.4 More books on Lie algebras and Lie groups 443
9.1.5 A.Borel,Linear Algebraic Groups,Second edition,Graduate Texts in Mathematics,126,Springer-Verlag,New York,1991.xii+288 pp 445
9.1.6 More books on algebraic groups,algebraic geometry and number theory 446
9.1.7 Algebraic invariant theories and representations of algebraic groups 450
9.1.8 E.Artin,Geometric Algebra,Reprint of the 1957 original,Wiley Classics Library,A Wiley-Interscience Publication,John Wiley＆Sons,Inc.,New York,1988.x+214 pp 452
9.1.9 J.Tits,Buildings of Spherical Type and Finite BN-pairs,Lecture Notes in Mathematics,Vol.38 6,Springer-Verlag,Berlin-New York,1974.x+299 pp 453
9.1.10 More books on buildings and finite geometries 454
9.1.11 Applications of Lie theories to differential equations 457
9.1.12 Discrete subgroups of Lie groups and algebraic groups 463
9.1.13 J.P.Serre,Trees,Translated from the French by John Stillwell,Springer-Verlag,Corrected 2nd printing of the 1980 English trans-lation,Springer Monographs in Mathematics,Springer-Verlag,Berlin,2003.x+142 pp 466
9.1.14 Discrete subgroups of low rank Lie groups and algebraic groups 467
9.1.15 Combinatorial groups and geometric group theory 469
9.1.16 Coxeter groups 474
9.1.17 Transformation groups 475
9.1.18 V.Kac,Infinite-dimensional Lie Algebras,Third edition,Cam-bridge University Press,Cambridge,1990.xxii+400 pp 479
9.1.19 Loop groups,quantum groups,Hopf algebras and vertex operator algebras 479
9.1.20 Applications of Lie groups in sciences 482
9.2 Representation theory 483
9.2.1 J.P.Serre,Linear Representations of Finite Groups,Translated from the second French edition by Leonard L.Scott,Graduate Texts in Mathematics,Vol.42 ,Springer-Verlag,New York-Heidelberg,1977.x+170 pp 484
9.2.2 I.G.Macdonald,Symmetric Functions and Hall Polynomials,Ox-ford Mathematical Monographs,The Clarendon Press,Oxford Uni-versity Press,New York,1979.viii+180 pp 484
9.2.3 Representation theory of the symmetric group 485
9.2.4 H.Weyl,The Classical Groups.Their Invariants and Represen-tations,Fifteenth printing,Princeton Landmarks in Mathematics,Princeton University Press,Princeton,NJ,1997.xiv+320 pp 487
9.2.5 Representation theories of Lie groups 489
10 Mathematical physics,dynamical systems and ergodic theory 495
10.1 Classical mathematical physics 495
10.1.1 R.Courant,D.Hilbert,Methods of Mathematical Physics.Vol.Ⅰ.,Vol.Ⅱ.,Interscience Publishers,Inc.,New York,1953.xv+561 pp..19 62.xxii+830 pp 496
10.1.2 H.Wleyl,The Theory of Groups and Quantum Mechanics,from the 2d rev.,German ed.,by H.P.Robertson,Dover Publications,1949.44 8 pp 497
10.1.3 L.D.Landau,E.M.Lifshitz,Course of Theoretical Physics.Vol.1.Mechanics,Third edition,Pergamon Press,Oxford-New York-Toronto,Ont.,1976.xxvii+169 pp 499
10.2 More modern mathematical physics 503
10.2.1 General relativity and gravitation 503
10.2.2 S.Hawking,G.Ellis,The Large Scale Structure of Space-time,Cambridge Monographs on Mathematical Physics,No.1 ,Cam-bridge University Press,London-New York,1973.xi+391 pp 506
10.2.3 Statistical mechanics 509
10.2.4 Quantum field theory 511
10.2.5 V.I.Arnold,Mathematical Methods of Classical Mechanics,Second edition,Graduate Texts in Mathematics,60,Springer-Verlag,New York,1989.xvi+508 pp 512
10.2.6 M.Reed,B.Simon,Methods of Modern Mathematical Physics.I.Functional Analysis.Second edition;Ⅱ.Fourier Analysis,Self-adjointness;Ⅲ.Methods of Modern Mathematical Physics;Ⅳ.Analysis of Operators,Academic Press,Inc.,New York,1980.xv+400 pp.,1975.xv+361 pp.,1979.xv+463 pp.,1978.xv+396 pp 514
10.2.7 Scattering theory 515
10.3 Dynamical systems 518
10.3.1 Dynamics and celestial mechanics 518
10.3.2 Dynamical systems 519
10.3.3 Infinite-dimensional dynamical systems 526
10.3.4 R.Thom,Structural Stability and Morphogenesis.An Outline of a General Theory of Models.Translated from the French by D.H.Fowler.With a foreword by C.H.Waddington,Advanced Book Classics,Addison-Wesley Publishing Company,Advanced Book Program,Redwood City,CA,1989.xxxvi+348 pp 529
10.3.5 Functional-differential equations 530
10.3.6 Complex dynamics 530
10.4 Ergodic theory 533
11 Discrete mathematics and combinatorics 537
11.1 Combinatorics 537
11.1.1 R.Stanley,Enumerative Combinatorics,Vol.Ⅰ.,Vol.2.,With a foreword by Gian-Carlo Rota,The Wadsworth＆Brooks/Cole Mathematics Series,1986.xiv+306 pp.,1999.xii+581 pp 538
11.1.2 Ploytopes,convex polytopes and geometric arrangements 539
11.1.3 Gr？bner bases 541
11.1.4 Matroid theory 542
11.1.5 L.Lovász.Combinatorial Problems and Exercises,Corrected reprint of the 1993 second edition,AMS Chelsea Publishing,Providence,RI,2007.6 42 pp 544
11.2 Discrete mathematics 545
11.2.1 J.Conway,N.Sloane,Sphere Packings,Lattices and Groups,Third edition,With additional contributions by E.Bannai,R.E.Borcherds,J.Leech,S.P.Norton,A.M.Odlyzko,R.A.Parker,L.Queen and B.B.Venkov,Grundlehren der Mathematischen Wissenschaften,290.Springer-Verlag,New York,1999.lxxiv+703 pp 545
11.2.2 Graph theory 546
11.2.3 Graphs and their spectra 551
11.2.4 Random graphs 552
12 Probability and applications 553
12.1 Probability 553
12.1.1 A.N.Kolmogorov,Foundations ofthe Theory ofProbability,Trans-lation edited by Nathan Morrison,with an added bibliography by A.T.Bharucha-Reid,Chelsea Publishing Co.,New York,1956.viii+84 pp.Translation of Grundbegriffe der Wahrscheinlichkeits-rechnung,Springer,Berlin,1933 554
12.1.2 W.Feller,An Introduction to Probability Theory and its Applica-tions,Vol.Ⅰ,Vol.Ⅱ.Third edition,John Wiley＆Sons,Inc.,New York-London-Sydney,1968.xviii+509 pp.,1971,xxiv+669 pp 555
12.1.3 More classical books on probability 556
12.1.4 More modern books on probability 558
12.1.5 Probability and analysis 559
12.1.6 More specialized books in probability 560
12.1.7 Random walks 562
12.2 Stochastic analysis 564
12.2.1 J.L.Doob,Stochastic Processes,Reprint of the 1953 original,Wiley Classics Library,A Wiley-Interscience Publication,John Wiley＆Sons,Inc.,New York,1990.viii+654 pp 565
12.2.2 Brownian motions and stochastic processes 567
12.2.3 Stochastic calculus and equations 572
12.2.4 Large deviations 574
12.2.5 Malliavin calculus 575
12.3 Applications of probability 576
12.3.1 Probabilistic methods and applications 576
12.3.2 Random matrices 580
13 Foundations of math,computer science,numerical math 583
13.1 Mathematical logic 583
13.1.1 Mathematical logic 584
13.1.2 D.Hofstadter,G？del,Escher,Bach:an Eternal Golden Braid,Basic Books,Inc.,Publishers,New York,1979.xxi+777 pp 586
13.1.3 B.Russell,Introduction to Mathematical Philosophy,Reprint of the 1920 second edition,Dover Publications,Inc.,New York,1993.viii+208 pp 586
13.1.4 Set theory 587
13.1.5 Model theory,non-standard analysis,recursive functions 591
13.2 Computer science 594
13.2.1 D.Knuth,The Art of Computer Programming.Vol.1 -Ⅳ,Second printing,Addison-Wesley Publishing Co.,1969.xxi+634 pp 595
13.2.2 R.Graham,D.Knuth,O.Patashnik,Concrete Mathematics.A Foundation for Computer Science,Second edition,Addison-Wesley Publishing Company,Reading,MA,1994.xiv+657 pp 595
13.2.3 T.Cover,J.Thomas,Elements of Information Theory,Second edi-tion,Wiley-Interscience[John Wiley＆Sons],Hoboken,NJ,2006.xxiv+748 pp 596
13.2.4 N.Wiener,Cybernetics,or Control and Communication in the An-imal and the Machine,Actualités Sci.Ind.,no.10 53,Hermann et Cie.,Paris;The Technology Press,Cambridge,Mass.;John Wiley＆Sons,Inc.,New York,1948.19 4 pp 597
13.2.5 M.Petkovsek,H.Wilf,D.Zeilberger,A=B,With a foreword by Donald E.Knuth,With a separately available computer disk,A K Peters,Ltd.,Wellesley,MA,1996.xii+212 pp 599
13.2.6 I.MacWilliams,N.Sloane,The Theory of Error-correcting Codes,Ⅰ,Ⅱ,North-Holland Mathematical Library,Vol.16.North-Holland Publishing Co.,Amsterdam-New York-Oxford,1977.pp.i-xv and 1-369.pp.i-ix and 370-762 600
13.2.7 More books on coding theory 601
13.2.8 Algorithm and automata 602
13.3 Game theory and optimization 604
13.3.1 J.von Neumann,O.Morgenstern,Theory of Games and Economic Behavior,Fourth printing of the 2004 sixtieth-anniversary edition,With an introduction by Harold W.Kuhn and an afterword by Ariel Rubinstein,Princeton University Press,Princeton,NJ,2007.xxxii+739 pp 605
13.3.2 More books on game theory and optimization 606
13.4 Numerical analysis and matrix computation 610
13.4.1 Numerical analysis 611
13.4.2 Finite element methods and finite difference methods 617
13.4.3 Approximation theory 620
Appendix A:Books in Chinese version 623
Appendix B:Books reprinted in the mainland of China 631
Index of books 643