Braids, links and representations of braid groups

This chapter presents an introduction to the theory of braids. The theory of braids has some nice intrinsically interesting properties which are worth studying. One can consider some functions looking like representations of braid groups and investigate their properties. It turns out that some of these functions have a good behaviour under A. A. Markov's moves. This idea was given to V.F.R. Jones by Joan Birman and led to the beautiful discovery of the Jones polynomial. While developing the idea that the Burau representation comes from some covering, Stephen Bigelow proposed a more sophisticated covering that leads to another representation. Bigelow proved its faithfulness by using the techniques of forks and noodles.