  We consider a version of the generalized hypergeometric system introduced by
Gelfand, Kapranov and Zelevinski (GKZ) suited for the case when the underlying
lattice is replaced by a finitely generated abelian group. In contrast to the
usual GKZ hypergeometric system, the rank of the better behaved GKZ
hypergeometric system is always the expected one. We give largely
self-contained proofs of many properties of this system. The discussion is
intimately related to the study of the variations of Hodge structures of
hypersurfaces in algebraic tori.
