Infinite Group Rings

The algebraic study of group rings was initiated in 1949 by I. Kaplansky. The subject has been pursued by a small but growing number of researchers, and has reached a point in its development where a coherent account of the basic results is needed. That is the goal of this text. The topics covered are selective, with material balanced between ring theory and group theory, and a basic one year course in algebra should provide sufficient background for readers.