  We analyze the U-duality group for the case of a type II superstring
compactified to four dimensions on a K3 surface times a torus. The various
limits of this theory are considered which have interpretations as type IIA and
IIB superstrings, the heterotic string, and eleven-dimensional supergravity,
allowing all these theories to be directly related to each other. The integral
structure which appears in the Ramond-Ramond sector of the type II superstring
is related to the quantum cohomology of general Calabi-Yau threefolds which
allows the moduli space of type II superstring compactifications on Calabi-Yau
manifolds to be analyzed.
