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.Comment: 40 Pages, Plain-TeX, no figure
