数学上，共变导数或称协变导数是在流形上定义沿着矢量场的导数的方法之一。

事实上，除了引入的风格不同之外，共变导数和联络没有实质上的区别。

在黎曼和伪黎曼流形理论中，共变导数通常指列维-奇维塔联系。

这里，我们给出一个矢量相对于矢量场的共变导数(也称为张量导数)的传统的带指标记号的简介；张量的共变导数是同一概念的推广。

本条目中，我们使用爱因斯坦记号。我们假设读者熟悉微分流形的概念特别是关于切矢量的概念。

In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection. In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean derivative along a tangent vector onto the manifold's tangent space. In this case the Euclidean derivative is broken into two parts, the extrinsic normal component and the intrinsic covariant derivative component.