  These are lecture notes of lectures presented at the 1993 Trieste Summer
School, dealing with two classes of two-dimensional field theories,
(topological) Yang-Mills theory and the G/G gauged WZW model. The aim of these
lectures is to exhibit and extract the topological information contained in
these theories, and to present a technique (a Weyl integral formula for path
integrals) which allows one to calculate directly their partition function and
topological correlation functions on arbitrary closed surfaces. Topics dealt
with are (among others): solution of Yang-Mills theory on arbitrary surfaces;
calculation of intersection numbers of moduli spaces of flat connections;
coupling of Yang-Mills theory to coadjoint orbits and intersection numbers of
moduli spaces of parabolic bundles; derivation of the Verlinde formula from the
G/G model; derivation of the shift k to k+h in the G/G model via the index of
the twisted Dolbeault complex.
