The Yang-Mills measure and symplectic structure over spaces of connections

A short overview is presented of : (i) the quantum field measure associated with pure Yang-Mills gauge theory on a compact surface, (ii) an approach to the symplectic structure on the [moduli] space of [flat] connections over compact oriented surfaces (with and without boundary), and (iii) the relation between the classical Yang-Mills measure and the volume measure on the moduli space of flat connections.