Chapter 1．K0 of Rings 1
1．Defining K0 1
2．K0 from idempotents 7
3．K0 of PIDs and local rings 11
4．K0 of Dedekind domains 16
5．Relative K0 and excision 27
6．An application:Swan's Theorem and topological K-theory 32
7．Another application:Euler characteristics and the Wall finiteness obstruction 41
Chapter 2．K1 of Rings 59
1．Defining K1 59
2．K1 of division rings and local rings 62
3．K1 of PIDs and Dedekind domains 74
4．Whitehead groups and Whitehead torsion 83
5．Relative K1 and the exact sequence 92
Chapter 3．K0 and K1 of Categories,Negative K-Theory 108
1．K0 and K1 of categories,G0 and G1 of rings 108
2．The Grothendieck and Bass-Heller-Swan Theorems 132
3．Negative K-theory 153
Chapter 4．Milnor's K2 162
1．Universal central extensions and H2 162
Universal central extensions 163
Homology of groups 168
2．The Steinberg group 187
3．Milnor's K2 199
4．Applications of K2 218
Computing certain relative K1 groups 218
K2 of fields and number theory 221
Almost commuting operators 237
Pseudo-isotopy 240
Chapter 5．The+-Construction and Quillen K-Theory 245
1．An introduction to classifying spaces 245
2．Quillen's+-construction and its basic properties 265
3．A survey of higher K-theory 279
Products 279
K-theory of fields and of rings of integers 281
The Q-construction and results proved with it 289
Applications 295
Chapter 6．Cyclic homology and its relation to K-Theory 302
1．Basics of cyclic homology 302
Hochschild homology 302
Cyclic homology 306
Connections with"non-commutative de Rham theory" 325
2．The Chern character 331
The classical Chern character 332
The Chern character on K0 335
The Chern character on higher K-theory 340
3．Some applications 350
Non-vanishing of class groups and Whitehead groups 350
Idempotents in C*-algebras 355
Group rings and assembly maps 362
References 369
Books and Monographs on Related Areas of Algebra,Analysis,Number Theory,and Topology 369
Books and Monographs on Algebraic K-Theory 371
Specialized References 372
Notational Index 377
Subject Index 383