  We construct the moduli of twisted sheaves on a projective variety. Then we
generalize known results on the moduli space of usual sheaves on a K3 surface
to the twisted case. Thus we consider the non-emptyness, the deformation type
and the Fourier-Mukai transformation. As an application of our results, Daniel
Huybrechts and Paolo Stellari prove Caldararu's conjecture.
