1. Topological tensor products and nuclear spaces
2."Continual" and "discrete" duality (derived categories and "six operations").
3.Yoga of the Grothendieck-Riemann-Roch theorem (K-theory, relation with intersection theory)
4.Schemes
5.Toposes
6.Etale cohomology including l-adic cohomology
7.Motives and the motivic Galois group (and Grothendieck categories)
8.Crystals and crystalline cohomology, yoga of De Rham and Hodge coefficients
9.Topological algebra, infinity-stacks, 'derivateurs', cohomological formalism
of toposes as an inspiration for a new homotopic algebra
10.Tame topology
11.Yoga of anabelian geometry and Galois-Teichmuller theory
12.Schematic point of view, or "arithmetics" for regular polyhedra and
regular configurations of all sorts
http://en.wikipedia.org/wiki/Alexander_Grothendieck