  We give an introductory review of topological strings and their application
to various aspects of superstrings and supersymmetric gauge theories. This
review includes developing the necessary mathematical background for
topological strings, such as the notions of Calabi-Yau manifold and toric
geometry, as well as physical methods developed for solving them, such as
mirror symmetry, large N dualities, the topological vertex and quantum foam. In
addition, we discuss applications of topological strings to N=1,2
supersymmetric gauge theories in 4 dimensions as well as to BPS black hole
entropy in 4 and 5 dimensions. (These are notes from lectures given by the
second author at the 2004 Simons Workshop in Mathematics and Physics.)
