Simplicial sheaves and presheaves, homology and cohomology, descent, localization and motivic homotopy theory, sheaves and presheaves of groupoids, stacks, cocycle categories, torsors, non-abelian cohomology.
lecture notes

Reading list:
1) P.G. Goerss and J.F. Jardine, "Simplicial Homotopy Theory", Progress in Mathematics Vol. 174, Birkhäuser Basel-Boston-Berlin (1999).
2) J.F. Jardine, "Stacks and the homotopy theory of simplicial sheaves", Homology, Homotopy and Applications 3(2) (2001), 361-384.
3) J.F. Jardine, "Cocycle categories", Preprint (2006), http://www.math.uwo.ca/~jardine/papers/preprints/index.shtml
4) J.F. Jardine, "Lectures on simplicial presheaves", http://www.math.uwo.ca/~jardine/papers/sPre/index.shtml
5) Fabien Morel and Vladimir Voevodsky. A^{1}-homotopy theory of schemes. Inst. Hautes Études Sci. Publ. Math., 90:45-143 (2001), 1999.