  A new approach to the quantization of Chern-Simons theory has been developed
in recent papers of the author. It uses a "simulation" of the moduli space of
flat connections modulo the gauge group which reveals to be related to a
lattice gauge theory based on a quantum group. After a generalization of the
formalism of q-deformed gauge theory to the case of root of unity, we compute
explicitely the correlation functions associated to Wilson loops (and more
generally to graphs) on a surface with punctures, which are the interesting
quantity in the study of moduli space. We then give a new description of
Chern-Simons three manifolds invariants based on a description in terms of the
mapping class group of a surface. At last we introduce a three dimensional
lattice gauge theory based on a quantum group which is a lattice regularization
of Chern-Simons theory.
