I was pleased to learn that MSRI and Cambridge University Press have decided to issue a second edition of this book. The first edition sold out its press run rather quickly, and for the last several years I have had regular inquiries from colleagues and students about where to obtain a copy.

The first edition was successful because it filled a need: there was nothing available at the time which even remotely covered the subject satisfactorily. Even now, while there are many more references available for this and related subjects, there is no other comprehensive treatment of the topics covered in this book, and so the second edition will (I hope) still fill an important need. Some of the newer references I can recommend to the reader are: [Fillmore 1996] and [Murphy 1990] as general references for C*-algebras, including some If-theory; [Davidson 1996] for a deep study of examples of important C*-algebras, including many treated superficially in my book; [Wegge-Olsen 1993] for a leisurely treatment of basic if-theory in more detail than we have included here; [Higson 1990] for a detailed survey of KK-theory and its applications, written primarily for nonspecialists in operator algebras; [Rosenberg 1994] for an excellent treatment of algebraic Ktheory; [Loday 1992] for cyclic homology/cohomology; and, of course, [Connes 1994] (which was already partially available at the time of the first edition)—its introduction gives a marvelous overview of the subject, and the book contains a vast supply of important applications. Several more books on operator Ktheory and related subjects are forthcoming.