During the two decades that preceded the publication of the first edition of this book, the GelfandKirillov dimension had emerged as a very useful and powerful tool for investigating noncommutative algebras. At that time, the basic ideas and results were scattered throughout various journal articles. The first edition of this book provided a muchneeded reliable and coherent single source of information. Since that time, the book has become the standard reference source for researchers. For this edition, the authors incorporated the original text with only minor modifications. Errors have been corrected, items have been rephrased, and more mathematical expressions have been displayed for the purpose of clarity. The newly added Chapter 12 provides broad overviews of the new developments that have surfaced in the last few years, with references to the literature for details. The bibliography has been updated and accordingly, almost double the size of the original one. The faithful revision and contemporary design of this work offers timehonored expertise with modern functionality: A keenly appealing combination. So, whether for the classroom, the welltended mathematical books collection, or the research desk, this book holds unprecedented relevance. Readership Advanced graduate students and research mathematicians interested in noncommutative algebra; mathematical physicists. Reviews "Has become a standard reference on the GelfandKirillov dimension ... The new Chapter 12 ... is of value because it is difficult to find it in the literature ... This book is a good exposition of the subject and it may serve as an introduction to it as well. The presentation is clear and contains many complete proofs."  Zentralblatt MATH "The appearance of a second edition signals that the book is good and interesting. This is certainly the case with the monograph under review ... it is very carefully and clearly written, and can be recommended not only to specialists, but to anybody who either intends to start working in this interesting field or needs some information concerning the GelfandKirillov dimension ... The book reads well, and the authors often mention the historical development of the subject and provide the text with many interesting examples."  European Mathematical Society Newsletter "The authors clearly had userfriendliness in mind in preparing this edition. Revisions have focused on clarification of presentation, the numbering of results from the original edition has been retained, and the new final chapter is organized so that Section 12.k gives updates relevant to Chapter k. The original bibliography has been expanded to about double its original length. This new edition will serve to continue to make this book a useful introduction to and reference in its field."  Mathematical Reviews Table of Contents  Introduction
 Growth of algebras
 GelfandKirillov dimension of algebras
 GelfandKirillov dimension of related algebras
 Localization
 Modules
 Graded and filtered algebras and modules
 Almost commutative algebras
 Weyl algebras
 Enveloping algebras of solvable Lie algebras
 Polynomial identitiy algebras
 Growth of groups
 New developments
 Bibliography
 Index
