# Introduction to Group Theory

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*Oleg Bogopolski*

A publication of the European Mathematical Society

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 & Endorsements

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