  These are the lecture notes for a short course in topological string theory
that I gave at Uppsala University in the fall of 2004. The notes are aimed at
PhD students who have studied quantum field theory and general relativity, and
who have some general knowledge of ordinary string theory. The main purpose of
the course is to cover the basics: after a review of the necessary mathematical
tools, a thorough discussion of the construction of the A- and B-model
topological strings from twisted N=(2,2) supersymmetric field theories is
given. The notes end with a brief discussion on some selected applications.
