代數K理論在代數拓撲、數論、代數幾何和算子理論等現代數學各個領域中的作用越來越大。這門學科的廣泛性往往使人感覺望而生畏。本書以1990年秋天Maryland大學講義為基礎，不僅為數學領域研究生提供很好的學習代數K理論的基本知識，也講述其在各個領域的應用。全書結構完整，了解代數基礎知識、基本代數拓撲和幾何拓撲知識就可以**讀懂這本書。該書也涉及到不少代數拓撲、拓撲代數和代數數論的知識。*後一章簡明地介紹了循環同調以及其與K理論的關繫。

Preface
Chapter 1.Ko of Rings
　1.Defining K0
　2.Ko from idempotents
　3.Ko of PIDs and local rings
　4.Ko of Dedekind domains
　5.Relative Ko and excision
　6.An application: Swan's Theorem and topological K- theory
　7.Another application: Euler characteristics and the Wall finiteness obstruction
Chapter 2.K1 of Rings
　1.Defining K1
　2.K1 of division rings and local rings
　3.K1 of PIDs and Dedekind domains
　4.Whitehead groups and Whitehead torsion
　5.Relative K1 and the exact sequence
Chapter 3.Ko and K1 of Categories, Negative K-Theory
　1.Ko and K1 of categories, Go and G1 of rings
　2.The Grothendieck and Bass-Heller-Swan Theorems
　3.Negative K-theory
Chapter 4.Milnor's K2
1.Universal central extensions and H2
Universal central extensions
　 Homology of groups
　2.The Steinberg group
　3.Milnor's K2
　4.Applications of K2
　 Computing certain relative K1 groups
　 K2 of fields and number theory
　 Almost commuting operators
　 Pseudo-isotopy
Chapter 5.The +-Construction and Quillen K-Theory
　1.An introduction to classifying spaces
　2.Quillen's +-construction and its basic properties
　3.A survey of higher K-theory
　 Products
　 K-theory of fields and of rings of integers
　 The Q-construction and results proved with it
　 Applications
Chapter 6.Cyclic homology and its relation to K-Theory
　1.Basics of cyclic homology
　　Hochschild homology
　　Cyclic homology
　　Connections with "non-commutative de Rhom theory"
　2.The Chern character
　　The classical Chern character
　　The Chern character on Ko
　　The Chern character on higher K-theory
　3.Some applications
　　Non-vanishing of class groups and Whitehead groups
　　Idempotents in C*-algebras
　　Group rings and assembly maps
References
　　Books and Monographs on Related Areas of Algebra,Analysis, Number Theory, and Topology
　　Books and Monographs on Algebraic K-Theory
　 Specialized References
Notational Index
Subject Index