A thorough introduction to group theory, this (highly problem-oriented) book goes deeply into the subject to provide a fuller understanding than available anywhere else. The book aims at, not only teaching the material, but also helping to develop the skills needed by a researcher and teacher, possession of which will be highly advantageous in these very competitive times, particularly for those at the early, insecure, stages of their careers. And it is organized and written to serve as a reference to provide a quick introduction giving the essence and vocabulary useful for those who need only some slight knowledge, those just learning, as well as researchers, and especially for the latter it provides a grasp, and often material and perspective, not otherwise available.

Contents:

• The Physical Principles of Group Theory
• Examples of Groups
• Groups as Mathematical Objects
• Groups, Combinations, Subsets
• Representations
• The Group as a Representation of Itself
• Properties of Representations
• The Symmetric Group and Its Representations
• Properties and Applications of Symmetric Groups
• The Rotation Groups and Their Relatives
• Representations of Groups SO(3) and SU(2)
• Applications of Representations of SO(3) and O(3)
• Lie Algebras
• Representations of Lie Algebras

"The manner and the style in which this purpose has been achieved distinguishes this book from many of the others in this area, which stands at the borders of the natural science ... The book is in fact for everyone — that is, everyone may find in it something nontrivial and fresh that deserves particular attention. Everyone will certainly be satisfied with it."