This is an introductory graduate-level course in additive combinatorics. Among topics that will be covered in the class are the following: discrete Fourier analysis over finite abelian groups; arithmetic progressions in the integers and finite abelian groups (Roth's theorem and the cap-set problem); Sidon sets; sum-free sets in the integers and finite abelian groups; sum-product estimates (the Erdős–Szemerédi conjecture); the Littlewood–Offord problem and singularity of random Bernoulli matrices; the structure of sets with a small sumset.

The course will be taught in English.