Topics in Algebraic and Topological K Theory This volume is an introductory textbook to K theory both algebraic and topological and to various current research topics within the field including Kasparovs bivariant K theory the Baum Connes conjecture the comparison between algebraic and topological K theory of topological algebras the K theory of schemes and the theory of dg categories K theory for group C* algebras Universal Coefficient Theorems and assembly maps in KK theory Algebraic v. topological K theory: a friendly match Higher algebraic K theory (after Quillen Thomason and others) Lectures on DG categories