  These are Lecture Notes of a course given by the author at the French-Spanish
School "Tresses in Pau", held in Pau (France) in October 2009. It is basically
an introduction to distinct approaches and techniques that can be used to show
results in braid groups. Using these techniques we provide several proofs of
well known results in braid groups, namely the correctness of Artin's
presentation, that the braid group is torsion free, or that its center is
generated by the full twist. We also recall some solutions of the word and
conjugacy problems, and that roots of a braid are always conjugate. We also
describe the centralizer of a given braid. Most proofs are classical ones,
using modern terminology. I have chosen those which I find simpler or more
beautiful.

Geometric Topology;Group Theory