Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.
"Classical" K-Theory.- The Plus Construction.- The Classifying Space of a Small Category.- Exact Categories and Quillen's Q-Construction.- The K-Theory of Rings and Schemes.- Proofs of the Theorems of Chapter 4.- Comparison of the Plus and Q-Constructions.- The Merkurjev-Suslin Theorem.- Localization for Singular Varieties.