A *homotopy* is a continuous transformation from one path in a topological space to another or more generally of one function to another.

Paths which are connected by a homotopy are called *homotopic* and are said to be in the same *homotopy class*.

Properties which are left unchanged by such homotopies are called *homotopy invariants*.

Homotoy classes of paths can be composed to form the fundamental group or *first homotopy group*. Other maps can be used to form *higher homotopy groups*.