The K-book: an introduction to algebraic K-theory

Algebraic K-theory is a field of abstract algebra concerning projective modules over a ring and vector bundles over schemes. It has many applications in mathematics such as algebraic topology and geometry, number theory and operator theory. In advanced physics there are applications such as string theory, D-brane theory and condensed matter physics. In this graduate level textbook Weibel presents the reader with a detailed overview of the field. Topics include Chern classes, Picard groups, Algebraic vector bundles, basic as well as more complex constructions of K0 and K1, as well as higher order K-groups Kn. There are many exercises at the end of each chapter and rigorous proofs throughout.