De Rham Cohomology is a mathematical tool used in the field of differential geometry and algebraic topology. It studies the properties of smooth manifolds by examining differential forms, which are mathematical objects that can be integrated over manifolds. The main idea is to analyze how these forms can be differentiated and how their integrals behave, leading to insights about the manifold's structure. The key concept in De Rham Cohomology is the notion of cohomology classes, which group together differential forms that are "equivalent" in a certain sense. This allows mathematicians to classify manifolds based on their topological features, such as holes and voids, providing a bridge between geometry and topology.