Ricci's Theorem is a fundamental result in the field of differential geometry, particularly concerning the behavior of Riemannian manifolds. It states that if a Riemannian manifold has a positive Ricci curvature, then it is compact and has a finite volume. This theorem helps mathematicians understand the geometric properties of spaces and their implications for the shape and structure of the universe. The theorem is named after the Italian mathematician Gregorio Ricci-Curbastro, who contributed significantly to the development of tensor calculus. Ricci's Theorem is essential in the study of general relativity, where the curvature of space-time is crucial for understanding gravitational effects.