Introduction and Motivation

These notes are an introduction to group actions on C*-algebras and their crossed products, primarily by discrete groups and with emphasis on situations in which the crossed products are simple and at least close to the class of C*-algebras expected to be classifiable in the sense of the Elliott program. They are aimed at graduate students who have had a one semester or one year course on the general theory of C*-algebras. (We give more details on the prerequisites later in this section.) These notes are not intended as a reference work. Our emphasis is on explaining ideas and methods, rather than on giving complete proofs. For some results, different proofs are given at different locations in these notes, or special cases are proved of results which are proved later in greater generality by quite different methods. For others, some of the main ideas are explained and simpler versions of some of the relevant lemmas are proved, but we refer to the research papers for the full proofs. Other results and calculations are left as exercises; the reader is strongly encouraged to do many of these, to develop facility with the material. Yet other results, needed for the proofs of the theorems described here but not directly related to dynamics, are quoted with only some general description, or with no background at all.