Quantum Field Theory in Curved Space-Time

These notes present an overview of the lectures held by Abhay Ashtekar on the theory of quantum fields in curved space-times and its applications to cosmology at the Summer School “Geometric, topological, and algebraic methods for quantum field theory”, held at Villa de Leyva in 2015. The first part of the notes is pretty much self contained, assuming only a basic knowledge of quantum field theory in Minkowski space-time, while the second part—more in the style of a seminar—presents applications to the theory of inflation.