Representation theory and character theory are basic tools for the study of the structure of finite groups. Based on the classical results by Frobenius, Burnside, and Schur, character theory makes a central contribution to the complete classification of finite simple groups. This book serves as a modern introduction to this important part of group theory.
The book gives in its first section a self-contained introduction to the character theory of finite groups, which can be used for a first lecture on the subject. Later sections concentrate on Clifford theory, that is the relations between characters of a group and its normal subgroups.
This theory has many applications for solvable groups. Character degrees and lengths of conjugacy classes are studied in detail. Isaacs’s theory of p-special characters is included with several applications. The text contains many recent results that are not published in previous books on the same subject.