  For each compact, simple, simply-connected Lie group and each integer level
we construct a modular tensor category from a quotient of a certain subcategory
of the category of representations of the corresponding quantum group. We
determine when at fractional levels the corresponding category is modular. We
also give a quantum version of the Racah formula for the decomposition of the
tensor product. This work relies on developing the basic representation theory
of quantum groups at roots of unity, including Harish-Chandra's Theorem. It
generalizes previous work which applied only to fractional levels or only to
the projective form of the group.
