This course introduces powerful probabilistic methods, and their applications to fundamental problems in extremal combinatorics. It includes an overview of classical probabilistic methods such as first- and second-moment methods and the Lóvasz local lemma, and of some fundamental notions and results in extremal combinatorics, such as set systems, sunflowers, antichains, graph partitions, and Turán-type problems. In addition, the course will treat a selection of related topics at the cutting-edge of research.
