  These are lecture notes prepared for a minicourse given at the Cimpa Research
School "Algebraic and geometric aspects of representation theory", held in
Curitiba, Brazil in March 2013. The purpose of the course is to provide an
introduction to the study of representations of braid groups. Three general
classes of representations of braid groups are considered: homological
representations via mapping class groups, monodromy representations via the
Knizhnik-Zamolodchikov connection, and solutions of the Yang-Baxter equation
via braided bialgebras. Some of the remarkable relations between these three
different constructions are described.
