The tangent space at a point p in an abstract manifold M can be described without the use of embeddings or coordinate charts. The elements of the tangent space are called tangent vectors, and the collection of tangent spaces forms the tangent bundle.

chain rule | coordinate chart | derivation algebra | differential k-form | directional derivative | Euclidean space | exterior algebra | Jacobian | Lie group | manifold | sheaf | tangent bundle | tangent space | vector field | velocity vector