Table of Contents

• Projective modules and vector bundles
• The Grothendieck group $K_0$ $K_1$ and $K_2$ of a ring
• Definitions of higher $K$-theory
• The fundamental theorems of higher $K$-theory
• The higher $K$-theory of fields
• Nomenclature
• Bibliography
• Index

About the Author

Charles A. Weibel, Rutgers University, New Brunswick, NJ, USA

Reviews

Charles Weibel's 'K-book' offers a plethora of material from both classical and more recent algebraic K-theory. It is a perfect source book for seasoned graduate students and working researchers who are willing and eager to follow the author's expository path and who are ready for a lot of additional reading and self-reliant work. The many instructive examples and clarifying remarks help the reader grasp the essentials of algebraic K-theory from a panoramic view, and the entire exposition represents a highly valuable and useful guide to the subject in all its diversity and topicality. Although barely being a textbook or neophyte in the field, despite the wealth of background material sketched wherever necessary, the book, under review, is certainly the most topical presentation of algebraic K-theory at this time and an excellent enhancement of the existing literature in any case." - Newsletter of the European Mathematical Society

"Weibel presents his important and elegant subject with the authority of an experienced insider, placing stresses where they should be, presenting motivations and characterizations (always succinctly) so as to familiarize the reader with the shape of the subject. ... it contains a great number of examples, woven beautifully into the narrative, and excellent exercises." - MAA Reviews