IntroSurvey of representation theory

Abstract

There could be thousands of Introductions/Surveys of representation theory, given that it is an enormous field. This is just one of them, quite personal and informal. It has an increasing level of difficulty; the first part is intended for final year undergrads. We explain some basics of representation theory, notably Schur-Weyl duality and representations of the symmetric group. We then do the quantum version, introduce Kazhdan-Lusztig theory, quantum groups and their categorical versions. We then proceed to a survey of some recent advances in modular representation theory. We finish with twenty open problems and a song of despair.