One of the most famous manifolds is the Mobius strip that helps us understand the possible structure of our universe and furthermore reality. A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be more complicated. In discussing manifolds, the idea of dimension  is important. For example, lines are one-dimensional, and planes two-dimensional.

In a one-dimensional manifold (or one-manifold), every point has a neighborhood that looks like a segment of a line. Examples of one-manifolds include a line, a circle, and two separate circles. In a two-manifold, every point has a neighborhood that looks like a disk. Examples include a plane, the surface of a sphere, and the surface of a torus.

Manifolds are important objects in mathematics and physics because they allow more complicated structures to be expressed and understood in terms of the relatively well-understood properties of simpler spaces.