1.1. Shimura varieties are like a brightly colored toy. The motivation for their study comes from considering moduli spaces of Hodge structures. LetX be a smooth, complex, projective variety of dimension n. The lattice Λ = H(X,Z)/torsion (the singular cohomology in middle degree) carries extra structures beyond that of a free abelian group, in virtue of the fact that X is a complex variety. (1)...