In this chapter we discussed Vandermonde matrices as an aid to fast matrix multiplication algorithms. They are useful in the title problem of the monograph at two points: in transforming an arbitrary precision algorithm into an exact one, and in transforming a partial matrix multiplication algorithm into a total one. The (classical) Vandermonde matrix is a special case of the confluent generalisation, so the algorithms that work on the latter can also be applied to the former. We therefore present the problem of the Vandermonde matrix using its confluent version. We have sketched its history back to 1901 and then listed a number of applications of this type of structured matrix. We have surveyed articles on the inversion of a confluent Vandermonde matrix and indicated the only two which together always work in quadratic time in the general case.