Introduction to the Language of Stacks and Gerbes

Abstract

This is the text of a series of four one hour lectures given as part of the “Third Lisbon Summer Lectures in Geometry”, which took place in the summer of 2002 at the Instituto Tecnico Superior in Lisbon. The lectures were aimed at an audience consisting of students with some background in topology (but not necessarily in algebraic geometry). The purpose of the lectures was to give a quick introduction to gerbes, with an emphasis on non-abelian ˇCech cohomology.