Szemerédi's Theorem is a fundamental result in combinatorial number theory that states any sufficiently large set of integers contains arbitrarily long arithmetic progressions. An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant, such as 2, 4, 6 or 5, 10, 15. The theorem was proven by Endre Szemerédi in 1975 and has significant implications in various areas of mathematics, including graph theory and additive combinatorics. It highlights the inherent structure within large sets of numbers, showing that patterns emerge even in seemingly random collections.