A First Course in Noncommutative Rings， an outgrowth of the author s lectures at the University of California at Berkeley， is intended as a textbook for a one-semester course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings， Jacobson s theory of the radical， representation theory of groups and algebras， prime and semiprime rings， primitive and semiprimitive rings， division rings， ordered rings， local and semilocal rings， perfect and semiperfect rings， and so forth. By aiming the level of writing at the novice rather than the connoisseur and by stressing the role of examples and motivation， the author has produced a text that is suitable not only for use in a graduate course， but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.