The study of shape, space, position, and measurement.
Euclidean geometry:: flat space governed by five postulates, the classical framework
non-Euclidean geometry:: curved spaces (hyperbolic, elliptic) where the parallel postulate fails
differential geometry:: uses calculus on manifolds, the language of relativity
Riemannian metric defines distance and curvature on smooth manifolds
symmetry and transformation groups connect geometry to algebra
projective geometry studies invariants under projection, central to computer vision
fractal geometry describes self-similar structures with non-integer dimension
Related:: topology, linear algebra, graph theory, optimization, quantum mechanics