Chapter 1. Algebras, modules, and representations
Chapter 2. Group representations and characters
Chapter 3. Characters and integrality
Chapter 4. Products of characters
Chapter 5. Induced characters
Chapter 6. Normal subgroups
Chapter 7. T.I. sets and exceptional characters
Chapter 8. Brauer’s theorem
Chapter 9. Changing the field
Chapter 10. The Schur index
Chapter 11. Projective representations
Chapter 12. Character degrees
Chapter 13. Character correspondence
Chapter 14. Linear groups
Chapter 15. Changing the characteristic

Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group.

The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging.