Main subject categories: • Ring Theory • Abstract Algebra[from Introduction to Volume II] A comprehensive introduction was furnished in Volume I, but a few comments are in order about the specific nature of Volume II.After a brief treatment of those techniques of homology and cohomology needed for rings, the book turns specifically to certain types of rings that have been objects of intense investigation in recent years-Azumaya algebras (5.3), rings with polynomial identity (Chapter 6), division rings, and, more generally, (finite dimensional) central simple algebras (Chapter 7), group rings (8.1 and 8.2), and enveloping algebras (8.3). Since the group ring contains all possible information about group representations and the enveloping algebra contains all possible information about Lie representations, these two types of rings have been unified in Chapter 8 under the heading, “Rings of Representation Theory”. These rings often are Noetherian, and the last part of Chapter 8 deals with general aspects of Noetherian theory that have been used in studying these rings (and also with Hopf algebras, another generalization).Although the general setup is the same as in Volume I, the pace of the text is somewhat faster than in the first volume. Indeed, the subjects of each chapter have had books devoted exclusively to them in the past, and to deal adequately with current research in any of these subjects would require several volumes.The goal in this volume has been to present a unified treatment to the reader and to give the reader some idea, at least, of research in ring theory of the 1980s.