We will start by reviewing the notion of Topological Quantum Field
Theory (TQFT) and its application to the study of three-manifolds and
of mapping class groups.  Then we will outline the properties of the
"Non semi-simple TQFTs" we constructed jointly with Christian
Blanchet, Nathan Geer and Bertrand Patureau.  We will also discuss
some of the analogies between our constructions and the recent work by
Bonahon and Wong on the representations of the skein algebra of a
surface.