# REPRESENTATION THEORY I.

**Brief introduction to the course:**

The course gives an introduction to the theory of group representations, in a manner that provides useful background for students continuing in diverse mathematical disciplines such as algebra, topology, Lie theory, differential geometry, harmonic analysis, mathematical physics, combinatorics.

**The goals of the course:**

Develop the basic concepts and facts of the complex representation theory of finite groups, compact toplogical groups, and Lie groups.

By the end of the course, students are enabled to do independent study and research in fields touching on the topics of the course, and how to use these methods to solve specific problems. In addition, they develop some special expertise in the topics covered, which they can use efficiently in other mathematical fields, and in applications, as well. They also learn how the topic of the course is interconnected to various other fields in mathematics, and in science, in general.

regular homework, and presentation or final

this course is prerequisite for Representation Theory II.