This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.

Review of the hardback:‘… this is a well written introduction to the theory of the algebraic K-groups Ko, K1 and K2; the author has done a wonderful job in presenting the material in a clear way that will be accessible to readers with a modest background in algebra.’

Franz Lemmermeyer Source: Zentralblatt MATH

Review of the hardback:‘This is a fine introduction to algebraic K-theory, requiring only a basic preliminary knowledge of groups, rings and modules.’

Source: European Mathematical Society

Review of the hardback:'… a fine introduction to algebraic K-theory …'

Source: EMS Newsletter

Review of the hardback:'… an excellent introduction to the algebraic K-theory.'

Source: Proceedings of the Edinburgh Mathematical Society