Non-Euclidean geometry is a type of geometry that is different from the traditional Euclidean geometry that is taught in schools. In Euclidean geometry, it is assumed that space is flat and straight lines are always parallel, but in non-Euclidean geometry, this is not always the case.

There are two main types of non-Euclidean geometry: hyperbolic geometry and elliptic geometry. In hyperbolic geometry, space is curved in such a way that parallel lines eventually diverge from each other. In elliptic geometry, space is curved in such a way that there are no parallel lines.

Non-Euclidean geometry has important applications in physics, particularly in the theory of relativity. It also has applications in other fields, such as architecture, art, and computer graphics.