This is the long awaited sequel to Lam's earlier GTM 131 "A First Course in Noncommutative Ring Theory" which received the following praise in the Monthly: "The book is beautifully written with many illuminating examples and exercises ... Reading Lam's book reminded me of my own delight in discovering the structure theory of rings and its applications ... I eagerly await Lam's second volume and confidently recommend his first." -Lance Small This new book can be read independently from the first volume and is intended to be used for lecturing, seminar- and self-study, and for general reference. It is focused more on specific topics in order to introduce the reader to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. This volume is particularly user-friendly with its abundance of examples illustrating the theory virtually at every step. A large number of carefully chosen exercises serves the dual purpose of providing practice to newcomers to the field, and offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way thereby introducing the reader to a considerable amount of interesting ring theory without being dragged through endless preparatory material.