The aim of the course is to present, to students in mathematics and in theoretical or mathematical physics, various constructions of 3 -manifold invariants inspired from the perturbative expansion of Chern-Simons theory. Some of these constructions rely on the surgery presentation of the manifold and are obtained in terms of the so-called Kontsevich integral. Other constructions are based on configuration-space integrals defined on the manifold itself.
The course will introduce all these techniques together with the relevant background (including finite-type knot invariants and Feynman diagrams). A basic knowledge of differential geometry and algebraic topology is however assumed.