Comment: Revised v2 from December 2019 corrects some errors in and adds some recent citations to v1 Revised v3 corrects a few typos in v2This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory
and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria
and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.