In this series of 4 lectures we discuss our recent proof (with Zaher Hani and Xiao Ma) on the long-time derivation of the Boltzmann equation, starting from hard sphere dynamics, under the Boltzmann-Grad scaling law. The proof relies on a layering argument, recursive formulas for cumulants, and construction and analysis of combinatorial structures called molecules. To facilitate participation by students with different backgrounds, the course will be preceded by two preparatory sessions reviewing the classical theory. Session 1 (Sergio Simonella): Thursday 12, 10:00-12:00 Session 2 (Mario Pulvirenti): Tuesday 17, 11:00-13:00 Lecture 1 (Yu Deng): Thursday 19, 10:00-12:00 Lecture 2 (Yu Deng): Tuesday 24, 11:00-13:00 Lecture 3 (Yu Deng): Thursday 26, 10:00-12:00 Lecture 4 (Yu Deng): Tuesday 31, 11:00-13:00