The primary purpose of the book is to highlight approximations to the difficult isomorphism problem in Coxeter groups. A number of theorems relating to this problem are stated and proven. Most of the results addressed here concern conditions which can be seen as varying degrees of uniqueness of representations of Coxeter groups. Throughout the investigation, the readers are introduced to a large number of tools in the theory of Coxeter groups, drawn from dozens of recent articles by prominent researchers in geometric and combinatorial group theory, among other fields. As the central problem of the book may in fact be solved soon, the book aims to go further, providing the readers with many techniques that can be used to answer more general questions. The readers are challenged to practice those techniques by solving exercises, a list of which concludes each chapter.

Contents:

• Preliminaries on Coxeter Groups
• Further Properties of Coxeter Groups
• Rigidity
• In the Beginning: Some Early Results
• Even Coxeter Groups
• More General Groups
• Refinements and Generalizations: Automorphisms and Artin Groups

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Readership: Graduate students in group theory and linear algebra, mathematicians.

"This well-written book presents many classes of Coxeter groups for which the isomorphism problem is solved. It provides an introduction to many if not all of the techniques that have been used in studying Coxeter groups."