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.