The course will be an introduction to the theory of model categories and abstract homotopy theory. After the basic definitions (model structures, homotopy categories, Quillen functors) we will study homotopy limits and colimits, some useful properties of model categories and their relation to $(\infty,1)$-categories. Time permitting we will talk about operads and the homotopy transfer theorem. Le lezioni saranno tutti i martedì di marzo, dalle 9:00 alle 11:00 e saranno disponibili anche in streaming al link https://meet.google.com/hhe-uzab-rqu