Vistoli's notes on descent, grothendieck topologies, fibered categories, and stacks at http://homepage.sns.it/vistoli/descent.pdf are not only just a really good introduction to algebraic stacks, they're some of the best notes I've ever read on any subject. What I really liked is that he took the time to not identify f*g* with (gf)*, which makes the proofs longer, but absolutely rigorous.

He starts with a review of category theory and classical scheme theory, then builds up grothendieck (pre)topologies, then builds up the notion of a fibered category, which is a generalization of a presheaf, then defines stacks in terms of presheaves fibered categories and descent. What's really great about this approach is that once you see how fibered categories work, Lurie's approach to higher topos theory ((infty,1)-categories generalize categories fibered in groupoids) makes a good deal more sense. I can't recommend it enough.

Vistoli's notes on descent, grothendieck topologies, fibered categories, and stacks at http://homepage.sns.it/vistoli/descent.pdf are not only just a really good introduction to algebraic stacks, they're some of the best notes I've ever read on any subject. What I really liked is that he took the time to not identify f*g* with (gf)*, which makes the proofs longer, but absolutely rigorous.

He starts with a review of category theory and classical scheme theory, then builds up grothendieck (pre)topologies, then builds up the notion of a fibered category, which is a generalization of a presheaf, then defines stacks in terms of presheaves and descent. What's really great about this approach is that once you see how fibered categories work, Lurie's approach to higher topos theory ((infty,1)-categories generalize categories fibered in groupoids) makes a good deal more sense. I can't recommend it enough.