A mini-course on topological strings

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.