Lectures on algebraic stacks
ALBERTO CANONACO

Abstract. These lectures give a detailed and almost self-contained introduction to algebraic stacks. A great part of the paper is devoted to preliminary technical topics, both from category theory (like Grothendieck topologies, fibred categories and stacks) and algebraic geometry (like faithfully flat descent). All this machinery is finally used to present the definition and some basic properties first of algebraic spaces and then of algebraic stacks

Rend. Mat. Appl. (7) 38 (2017) 1-169; pdf