A decomposition of a space E into a family of identical subspaces (fibers). The space of subspaces is called the base space. Fiber bundles arise naturally in many physical situations. The theory of fiber bundles has been applied to gauge theory in physics, and there is a lively interaction centered on ideas related to fiber bundles and gauge theories in which significant results have been contributed in both areas. The development of the mathematical theory of fiber bundles was begun in the 1930s and has numerous applications within mathematics.