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-Kahler manifolds, the book includes a detailed discussion on the applications of the general theory to the two main example series of compact hyper-K?hler manifolds: the Hilbert schemes of points on a K3 surface and the generalized Kummer varieties.