A branch of topology that deals with the notion of a fiber bundle.

In topology, a branch of mathematics, a fibration is a generalization of the notion of a fiber bundle. A fiber bundle makes precise the idea of one topological space (called a fiber) being "parameterized" by another topological space (called a base). A fibration is like a fiber bundle, except that the fibers need not be the same space, rather they are just homotopy equivalent. (Wikipedia)

Further reading : Fibre bundles