  The purpose of this paper is to put into a noncommutative context basic
notions related to vector fields from classical differential geometry. The
manner of exposition is an attempt to make the material as accessible as
possible to classical geometers. The definition of vector field used is a
specialisation of the Cartan pair definition, and the paper relies on the idea
of generalised braidings of 1-forms. The paper considers Kroneker deltas,
interior products, Lie derivatives, Lie brackets, exponentiation of vector
fields and parallel transport.
