  The primary purpose of these lecture notes is to explore the moduli space of
type IIA, type IIB, and heterotic string compactified on a K3 surface. The main
tool which is invoked is that of string duality. K3 surfaces provide a
fascinating arena for string compactification as they are not trivial spaces
but are sufficiently simple for one to be able to analyze most of their
properties in detail. They also make an almost ubiquitous appearance in the
common statements concerning string duality. We review the necessary facts
concerning the classical geometry of K3 surfaces that will be needed and then
we review "old string theory" on K3 surfaces in terms of conformal field
theory. The type IIA string, the type IIB string, the E8 x E8 heterotic string,
and Spin(32)/Z2 heterotic string on a K3 surface are then each analyzed in
turn. The discussion is biased in favour of purely geometric notions concerning
the K3 surface itself. These are an extended form of the notes from lectures
given at TASI 96.
