  These notes of a course given at IRMA in April 2009 cover some aspects of the
representation theory of fundamental groups of manifolds of dimension at most 3
in compact Lie groups, mainly $\su$. We give detailed examples, develop the
techniques of twisted cohomology and gauge theory. We review Chern-Simons
theory and describe an integrable system for the representation space of a
surface. Finally, we explain some basic ideas on geometric quantization. We
apply them to the case of representation spaces by computing Bohr-Sommerfeld
orbits with metaplectic correction.
