By Kenneth R. Davidson

The topic of C*-algebras acquired a dramatic revitalization within the Nineteen Seventies by way of the creation of topological tools throughout the paintings of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of $K$-theory to supply an invaluable category of AF algebras. those effects have been the start of a fabulous new set of instruments for interpreting concrete C*-algebras.

This e-book is an introductory graduate point textual content which offers the fundamentals of the topic via a close research of a number of very important periods of C*-algebras. the advance of operator algebras within the final two decades has been in accordance with a cautious research of those exact periods. whereas there are numerous books on C*-algebras and operator algebras to be had, this is often the 1st one to try to give an explanation for the genuine examples that researchers use to check their hypotheses. subject matters comprise AF algebras, Bunce-Deddens and Cuntz algebras, the Toeplitz algebra, irrational rotation algebras, staff C*-algebras, discrete crossed items, abelian C*-algebras (spectral idea and approximate unitary equivalence) and extensions. It additionally introduces many sleek techniques and ends up in the topic corresponding to actual rank 0 algebras, topological strong rank, quasidiagonality, and numerous new buildings.

These notes have been compiled in the course of the author's participation within the precise 12 months on C*-algebras on the Fields Institute for learn in Mathematical Sciences throughout the 1994-1995 educational yr. the sphere of C*-algebras touches upon many different parts of arithmetic equivalent to team representations, dynamical structures, physics, $K$-theory, and topology.