A Riemannian manifold is a type of geometric space that combines the concepts of differential geometry and topology. It is a smooth manifold equipped with a Riemannian metric, which allows for the measurement of distances and angles. This metric provides a way to define notions like curvature, enabling the study of geometric properties and the behavior of curves and surfaces within the manifold. Riemannian manifolds are named after the mathematician Bernhard Riemann, who contributed significantly to the field of geometry. They are essential in various areas of mathematics and physics, including general relativity, where they describe the curvature of spacetime.