数学上，矢量丛是一个几何构造，为拓扑空间（或流形，或代数簇）的每一点兼容地附上一个矢量空间，而这些矢量空间“粘起来”又构成一个拓扑空间（或流形，或代数簇）。 一个典型的例子是微分流形（Differentiable manifold）的切丛：对流形的每一点附上流形在该点的切空间。 另一个例子是法丛：给定一个平面上的光滑曲线，可在曲线的每一点附上和曲线垂直的直线；这就是曲线的"法丛"。

这个条目主要解释有限维纤维的实矢量丛。复矢量丛也在很多地方有用；他们可以视为一种有附加结构的实矢量丛。

矢量丛是纤维丛的一种。

In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X.