L. Rozansky and E. Witten associated to any hyper-Kaehler manifold a system of "weights" (numbers, one for each trivalent graph) and used them to construct invariants of topological 3-manifolds. We will give Kapranov´s definition of Rozansky-Witten invariants and discuss their links to characteristic classes of foliations and the Gelfand-Fuks cohomology. We will follow closely papers: arXiv:alg-geom/9704009 and arXiv:dg-ga/9704009.

Part I by Alex, Part B by Vasily after the break