The Bott Periodicity Theorem is a fundamental result in algebraic topology, particularly in the study of stable homotopy theory. It states that the homotopy groups of the unitary groups, denoted as U(n), exhibit periodic behavior as n increases. Specifically, the theorem reveals that these groups repeat every eight dimensions, which means that the properties of these groups can be understood by examining only a finite number of cases. This theorem was first proven by mathematician Raoul Bott in the 1950s and has significant implications in various areas of mathematics, including K-theory and index theory. The periodicity provides a powerful tool for understanding the structure of vector bundles and their associated topological properties, making it a cornerstone in modern topology.