he primary topic of this work is the solution of string theories compactified on a Calabi-Yau manifold. The prepotentials and the geometry of the moduli spaces for a Calabi-Yau manifold and its mirror are computed. In this way all sigma model corrections to the Yukawa couplings and moduli space metric for the original manifold are obtained. The moduli space is found to be subject to the action of a modular group which, among other operations, exchanges large and small values of the radius though the action on the radius is not as simple as R... |