A fiber bundle is the most general kind of bundle. Special cases are often described by replacing the word "fiber" with a word that describes the fiber being used, e.g., vector bundles and principal bundles.

A fiber bundle is a structure $(E, B, π, F)$, where $E,$ $B$, and $F$ are topological spaces and $π : E → B$ is a continuous surjection satisfying a local triviality condition outlined below. The space $B$ is called the base space of the bundle, $E$ the total space, and $F$ the fiber. The map $π$ is called the projection map (or bundle projection). We shall assume in what follows that the base space B is connected.