Complex sentence: This article presents a traditional introduction, using a coordinate system, to the covariant derivative of a vector with respect to a vector field; the covariant derivative of a tensor field is an extension of the same concept.
Split into simpler sentences: This article presents a traditional introduction, using a coordinate system, to the covariant derivative of a vector field with respect to a vector. The covariant derivative of a tensor field is an extension of the same concept.