1
Grothendieck Topologies
Grothendieck topologies, sites, sheaves on a site, and standard examples
2
Stacks
Groupoids, categories fibered in groupoids, descent, and the definition of a stack
3
Algebraic Stacks
Artin and Deligne-Mumford stacks via atlases, and quotient stacks
4
Moduli Spaces
Moduli functors, fine and coarse moduli spaces, and why the moduli stack is the right object
5
Proper Stacks
Proper Deligne–Mumford stacks, their valuative criterion, and coarse moduli spaces
6
Integration on Deligne–Mumford Stacks
Rational Chow groups, proper pushforward, and integration on Deligne–Mumford stacks