Hodge Decomposition is a mathematical theorem in the field of differential geometry and topology. It states that any smooth differential form on a compact Riemannian manifold can be uniquely decomposed into three components: an exact form, a co-exact form, and a harmonic form. This decomposition helps in understanding the structure of differential forms and their relationships. The significance of Hodge Decomposition lies in its applications across various areas, including mathematical physics, algebraic topology, and fluid dynamics. It provides tools for solving partial differential equations and analyzing the properties of manifolds, making it a fundamental concept in modern mathematics.