Table of Contents

General notation
Introduction
Part I: C*-algebras
1: C*-algebras - a summary
2: Multiplier algebras
3: Extensions of C*-algebras
4: Invertibles and unitaries
5: Projections
Part II: Fundamentals of K-Theory
6: K0-basic properties
7: K1 and suspensions
8: The index map in K-theory
9: Bott periodicity
10: K-theory for multiplier algebras
11: Homology
12: Some examples: AF-algebras, Cuntz algebras, rotation algebras
13: Vector bundles and topological K-theory
Part III: Hilbert Modules and a Generalized Index Theory
14: The classical Fredholm index
15: Hilbert modules
16: The Kuiper-Mingo theorem
17: A generalized Fredholm index
Part IV: Appendices
G: The Grothendieck group
L: Inductive limits
O: (Dis)order and positivity in C*-algebras
T: Tensor products -or: the importance of being subcross
References
Subject index

Reviews

'no details are left out in the presentation, and many instructive and generously hinted exercises are provided'
L'Enseignement Mathématique, 3-4 1993
`... it is written in a very lively and user friendly style... Altogether I think this book is very recommendable as a first introduction to the subject.'
Monatshefte fur Mathematik, 3 April 1995