A sumset is a mathematical concept that involves the addition of elements from two sets. Specifically, if you have two sets, A and B, the sumset, denoted as A + B, consists of all possible sums formed by taking one element from A and one element from B. For example, if A = 1, 2 and B = 3, 4, the sumset A + B would be 4, 5, 6. Sumsets are useful in various areas of mathematics, including number theory and combinatorics. They help in understanding how different sets interact through addition and can lead to insights about the properties of numbers. The study of sumsets can also relate to concepts like group theory and finite fields, making them a valuable tool in advanced mathematical research.