# Definition > The *tangent bundle* is a $2n$ dimensional [[Fiber Bundle]] whose base [[manifold]] is an n-dimensional manifold $M$ and the fibers are the [[tangent spaces]] at every point $P \in M$. It can be written as: > $ TM = \bigcup_{x \in M} \{(x, y), y \in T_x M\} $ > It is an example of a [[Vector Bundle]].