  We study certain moduli spaces of sheaves on Enriques surfaces thereby
obtaining, in every odd dimension, new examples of Calabi-Yau manifolds. We
describe the geometry (canonical bundle, fundamental group, second Betti number
and certain Hodge numbers) of these moduli spaces showing, in partial analogy
to the well-known case of sheaves on K3 or Abelian surfaces, how the geometry
of the surface reflects that of the moduli space itself.
