This book quickly introduces beginners to general group theory and then focuses on three main themes :

• finite group theory, including sporadic groups
• combinatorial and geometric group theory, including the Bass-Serre theory of groups acting on trees
• the theory of train tracks by Bestvina and Handel for automorphisms of free groups

With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples.

Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Undergraduates, graduate students, and research mathematicians interested in group theory.

Reviews

"The book can be used for a graduate course in group theory, but it can also be read independently. In both cases, the student that manages to work through the book in detail will be rewarded with a working knowledge of advanced, mainstream topics in group theory."

-- MAA Reviews

Table of Contents

• Introduction to finite group theory
• Introduction to combinatorial group theory
• Automorphisms of free groups and train tracks
• Appendix. The Perron-Frobenius Theorem
• Solutions to selected exercises
• Bibliography
• Index