  We consider in general terms dynamical systems with finite-dimensional,
non-simply connected configuration-spaces. The fundamental group is assumed to
be finite. We analyze in full detail those ambiguities in the quantization
procedure that arise from the non-simply connectedness of the classical
configuration space. We define the quantum theory on the universal cover but
restrict the algebra of observables $\O$ to the commutant of the algebra
generated by deck-transformations. We apply standard superselection principles
and construct the corresponding sectors. We emphasize the relevance of all
sectors and not just the abelian ones.
