The Atiyah-Bott Theorem is a fundamental result in mathematics that connects topology and geometry, particularly in the study of vector bundles over manifolds. It provides a way to compute the dimensions of certain spaces of sections of vector bundles, which are essential in understanding the properties of manifolds. This theorem is named after mathematicians Michael Atiyah and Raoul Bott, who developed it in the 1980s. It has significant implications in various fields, including algebraic geometry and mathematical physics, as it helps in analyzing the behavior of geometric objects and their associated functions.