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This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within
the field, including Kasparov´s 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.

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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

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