The space of gauge equivalence classes of flat connections on a 2-manifold of genus g≥2 has attracted a great deal of attention in the mathematical literature since the landmark 1982 paper of Atiyah and Bott. It is a finite-dimensional symplectic manifold of dimension 6g − 6. I will describe Atiyah and Bott’s results on its Betti numbers as well as results on the ring structure of the cohomology (due to myself and Frances Kirwan, following Witten.