Introduction to Group Theory

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.