Content: Recent advances in stable homotopy theory and algebraic geometry use the language of higher category theory. The lecture will give an introduction to the theory of infinity-categories, stable infinity-categories and the generalization of classical algebra to these contexts, as developed by Jacob Lurie.

Prerequisites: We assume familiarity with basic concepts from topology and homotopy theory.

Detailed Information can be found on the Homepage of 19219401 Higher algebra.

Literature:

• Jacob Lurie: Higher Topos Theory. Annals of Mathematics Studies 170, Princeton University Press 2009
• Jacob Lurie: Higher Algebra; available from the authors homepage