This set of notes of the Geometry Seminar held at Ecole Polytechnique in the fall of 1981 is devoted to the geometry of K3 surfaces. This subject which has already a long history developed very quickly in recent years. It shows an interesting interplay between techniques of both differential and algebraic geome-try. The period mapping gives a nice parametrization of the moduli space thanks to appropriate Torelli theorems (both local and global). These notes include also a simplified proof of the fact that any K3 surface is kahlerian ( a theorem of Y.T.Siu). Examples of higher dimensional complex manifolds with vanishing first Chern class generalizing appropriately K3 surfaces are also presented. These notes have been kept as self-contained as possible in order to make the subject accessible to non-specialists.