This unique book deals with the theory of Rozansky-Witten invariants, introduced by L Rozansky and E Witten in 1997. It covers the latest developments in an area where research is still very active and promising. With a chapter on compact hyper-Kähler manifolds, the book includes a detailed discussion on the applications of the general theory to the two main example series of compact hyper-Kähler manifolds: the Hilbert schemes of points on a K3 surface and the generalized Kummer varieties.