Riemannian geometry is a branch of mathematics that deals with the geometry of curved surfaces and spaces. It was developed by the German mathematician Bernhard Riemann in the 19th century. Synonyms for Riemannian geometry include non-Euclidean geometry and differential geometry. These terms refer to the fact that the geometry of Riemannian surfaces and spaces is different from that of Euclidean geometry, which deals with flat, two-dimensional surfaces. Other related terms include Riemann geometry, Riemannian manifold, and Riemannian space. All these terms are used interchangeably to describe the same field of mathematics, which has practical applications in physics, engineering, and computer science.