K-theory Books - Free eBooks Directory

These lecture notes contain an exposition of basic ideas of K-theory and cyclic cohomology. I begin with a list of examples of various situations in which the K-functor of Grothendieck appears naturally, including the rudiments of the topological and algebraic K-theory, K-theory of C*-algebras, and K-homology. ...

Algebraic K-theory is an important part of homological algebra. From the 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.

We present 18 Introductory Lectures on K-Theory covering its basic three branches, namely topological, analytic (K-Homology) and Higher Algebraic K-Theory, 6 lectures on each branch. 

Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring A instead of over a field.

The algebraic K-theory presented here is, essentially, a part of general linear algebra. It is concerned with the structure theory of projective modules, and of their automorphism groups.