An introduction to braid groups

We will give an introductory talk on the braid group. This group can be thought of in (at least) three ways: algebraically (via a presentation by generators and relations) or geometrically (as the fundamental group of a certain manifold, or as the mapping class group of a certain surface). These three different perspectives generalize in three different ways. Time permitting, I will discuss the word problem for braid groups, some relations between braids and knot theory, and some aspects of the representation theory of the braid group.