  These lectures, given at the 1992 Trieste Spring School, are devoted to some
selected topics in N=2 \sm s on Calabi-Yau manifolds and the associated N=2
superconformal field theories. The first lecture is devoted to the ``special
geometry" of the moduli space of $c=9$ N=2 superconformal field theories. An
important role is played by the extended chiral algebra which appears in
theories with integer $U(1)$ charges. The second lecture is devoted to the \sm\
approach. The main focus is an explication of a calculation of Aspinwall and
Morrison.
