  This is a very brief survey of some results in the geometry of string duality
delivered at a lecture given at ICM 1998, Berlin. String Duality is the
statement that one kind of string theory compactified on one space is
equivalent in some sense to another string theory compactified on a second
space. This draws a connection between two quite different spaces. Mirror
symmetry is an example of this. Here we discuss mirror symmetry and another
``heterotic/type II'' duality which relates vector bundles on a K3 surface to a
Calabi-Yau threefold.
