The course serves as an introduction to the theory of group representations and its applications. Representation theory was born at the end of the XIXth century, and quickly became the fundamental tool in studying the structure of symmetries in mathematics and in the sciences in general.

Contents

1. Characters and the representation theory of finite groups. 

2. Real and complex representations.
3. Representations of the permutation group.
4. Examples of matrix group representations.

Cours en anglais ou en français selon la demande des étudiants.