  These are notes based on lectures given at TASI99. We review the geometry of
the moduli space of N=2 theories in four dimensions from the point of view of
superstring compactification. The cases of a type IIA or type IIB string
compactified on a Calabi-Yau threefold and the heterotic string compactified on
K3xT2 are each considered in detail. We pay specific attention to the
differences between N=2 theories and N>2 theories. The moduli spaces of vector
multiplets and the moduli spaces of hypermultiplets are reviewed. In the case
of hypermultiplets this review is limited by the poor state of our current
understanding. Some peculiarities such as ``mixed instantons'' and the
non-existence of a universal hypermultiplet are discussed.
