Hodge Theory is a branch of mathematics that studies the relationship between algebraic topology and differential geometry. It focuses on the decomposition of differential forms on a smooth manifold, allowing mathematicians to understand the structure of these forms in terms of simpler components. This theory connects various mathematical concepts, such as cohomology and harmonic forms, providing insights into the topology of manifolds. One of the key results of Hodge Theory is the Hodge decomposition theorem, which states that any differential form can be uniquely expressed as the sum of an exact form, a co-exact form, and a harmonic form. This decomposition helps in solving problems related to the geometry and topology of manifolds, making Hodge Theory a vital tool in modern mathematics.