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 relate to the original sets. This field often explores questions about the structure and distribution of these sums, leading to insights in number theory and related areas. One of the key concepts in additive combinatorics is the Cauchy-Davenport theorem, which provides bounds on the size of the sumset of two finite sets of integers. Researchers in this field also investigate arithmetic progressions and Freiman's theorem, which connects additive properties to the structure of sets, revealing deeper relationships within number systems.