  These are notes of my lectures given at the school on intersection theory and
moduli at the ICTP, Trieste. We construct moduli spaces of K3 surfaces and
higherdimensional hyperkaehler manifolds, including moduli spaces of
(2,2)-conformal field theories associated to hyperkaehler manifolds, and
describe their period domains. Recent results on these manifolds are discussed
from the moduli space point of view. The second goal is to present a detailed
account of mirror symmetry for K3 surfaces. Arguments due to Aspinwall and
Morrison allow one to explain various versions of mirror symmetry (e.g. for
lattice polarized or elliptic K3 surfaces) by the same general principle.
