This is the first in a series of lectures on quantum field theory aimed at mathematicians studying geometry/topology. The main purpose of the lecture series will be to work through Costello´s book 'Renormalization and Effective Field Theory' in gory detail, although I will begin by motivating the book by discussing other flavors of QFT as well as the history of the subject.

Prerequisites are the standard graduate material in analysis, geometry, and homological algebra, but I will also assume familiarity with simplicial sets, the asymptotic expansion of the heat kernel, and (classical) gauge theory.