Additive Combinatorics is a branch of mathematics that studies the additive properties of sets of numbers. It focuses on understanding how subsets of integers can combine to form new sums and how these sums behave under various conditions. This field often involves concepts from number theory, group theory, and combinatorial geometry. One of the key areas of research in Additive Combinatorics is the study of arithmetic progressions within sets of integers. A famous result in this area is Szemerédi's theorem, which states that any sufficiently large subset of integers contains arbitrarily long arithmetic progressions. This theorem highlights the deep connections between additive structures and combinatorial properties.