  These lectures are devoted to introducing some of the basic features of
quantum geometry that have been emerging from compactified string theory over
the last couple of years. The developments discussed include new geometric
features of string theory which occur even at the classical level as well as
those which require non-perturbative effects. These lecture notes are based on
an evolving set of lectures presented at a number of schools but most closely
follow a series of seven lectures given at the TASI-96 summer school on
Strings, Fields and Duality.
