  This thesis studies the pre-quantization of quasi-Hamiltonian group actions
from a cohomological viewpoint. The compatibility of pre-quantization with
symplectic reduction and the fusion product are established, and are used to
understand the sufficient conditions for the pre-quantization of $M_G(\Sigma)$,
the moduli space of flat $G$-bundles over a closed surface $\Sigma$. For a
simply connected, compact, simple Lie group $G$, $M_G(\Sigma)$ is known to be
pre-quantizable at integer levels. For non-simply connected $G$, however,
integrality of the level is not sufficient for pre-quantization, and this
thesis determines the obstruction---namely a certain cohomology class in
$H^3(G\times G;\Z)$---that places further restrictions on the underlying level.
The levels that admit a pre-quantization of the moduli space are determined
explicitly for all non-simply connected, compact, simple Lie groups $G$.
Partial results are obtained for the case of a surface $\Sigma$ with marked
points. Also, it is shown that via the bijective correspondence between
quasi-Hamiltonian group actions and Hamiltonian loop group actions, the
corresponding notions of pre-quantization coincide.
