Braids, links and representations of braid groups

In the previous chapters, we considered only one way of encoding links, namely, link planar diagrams.1 In the present chapter, we are going to give an introduction to the theory of braids. On one hand, this theory gives us another point of view to knot theory. On the other hand, the theory of braids has some nice intrinsically interesting properties which are worth studying. Namely, the braid groups can be defined in many ways that lead to connections with different theories. Below, we are going to give some definitions of the braid groups and to discuss some properties of them.