Poisson structure and quantization of Chern-Simons theory

In this note we review some work on the Poisson structure and on the quantization of 2+1 dimensional Chern-Simons theory or, in more mathematical terms, of the moduli space of flat connections over a 2-dimensional surface Sigma. This moduli space is one of the most important examples of a singular symplectic space. Our description focuses on the combinatorial approach in which the surface Sigma is replaced by a fat graph. Due to the topological nature of the theory, this finite model is exact and allows to recover a number of important results on Chern-Simons theory.