- Algebraic K-theory. Classical calculations related to zeta functions and etale cohomology, and applications to Algebraic Geometry. For more details, see my K-book (AMS Grad. Texts in Math).
- Motivic Cohomology. Applications to K-theory and Algebraic Geometry. For an introduction to this subject, see my book with Mazza and Voevodsky, Lectures on Motivic Cohomology (Clay Math Monographs 2, 2006.
- Motivic homotopy theory. Algebraic cobordism and homotopy groups.
- Cyclic Homology. Kahler differentials on singular varieties, applications to K-theory.
- Algebraic Geometry: Calculations of Chow groups of singular varieties. Zero-cycles on surfaces of general type.
- Homological Algebra. See my book "An introduction to Homological Algebra" (Cambridge U. Press, 1994).