  We review the structure of the moduli space of particular N = (2,2)
superconformal field theories. We restrict attention to those of particular use
in superstring compactification, namely those with central charge c = 3d for
some integer d and whose NS fields have integer U(1) charge. The cases d = 1, 2
and 3 are analyzed. It is shown that in the case d >= 3 it is important to use
techniques of algebraic geometry rather than rely on metric-based ideas. The
phase structure of these moduli spaces is discussed in some detail. (Lectures
Delivered at Trieste Summer School, 1994.)
