Geometry

In common parlance, geometry refers to a branch of mathematics that studies the relationships between figures such as e.g. points, lines, triangles, balls, vectors, surfaces and others in a space, such as plane, a higher dimensional Euclidean space, a sphere or, more generally, a manifold.

As a mathematical term, geometry refers to either the spatial (metric) properties of a given space or, more specifically in differential geometry, a given complete locally homogeneous Riemannian manifold.