Chapter One：Preliminaries 1
Section 1．Notation and terminology 1
Section 2．Group theory 3
Section 3．Topology 9
Chapter Two：Elements of the theory of topological groups 15
Section 4．Basic definitions and facts 16
Section 5．Subgroups and quotient groups 32
Section 6．Product groups and projective limits 52
Section 7．Properties of topological groups involving connectedness 60
Section 8．Invariant pseudo-metrics and separation axioms 67
Section 9．Structure theory for compact and locally compact Abelian groups 83
Section 10．Some special locally compact Abelian groups 106
Chapter Three：Integration on locally compact spaces 117
Section 11．Extension of a linear functional and construction of a measure 118
Section 12．The spaces ？p（X）（1？p？∞） 135
Section 13．Integration on product spaces 150
Section 14．Complex measures 166
Chapter Four：Invariant functionals 184
Section 15．The Haar integral 184
Section 16．More about Haar measure 215
Section 17．Invariant means defined for all bounded functions 230
Section 18．Invariant means on almost periodic functions 245
Chapter Five：Convolutions and group representations 261
Section 19．Introduction to convolutions 262
Section 20．Convolutions of functions and measures 283
Section 21．Introduction to representation theory 311
Section 22．Unitary representations of locally compact groups 335
Chapter Six：Characters and duality of locally compact Abelian groups 355
Section 23．The character group of a locally compact Abelian group 355
Section 24．The duality theorem 376
Section 25．Special structure theorems 399
Section 26．Miscellaneous consequences of the duality theorem 426
Appendix A：Abelian groups 439
B：Topological linear spaces 451
C：Introduction to normed algebras 469
Bibliography 492
Index of symbols 506
Index of authors and terms 509