  We prove local uniformization of Abhyankar valuations of an algebraic
function field K over a ground field k. Our result generalizes the proof of
this result, with the additional assumption that the residue field of the
valuation ring is separable over k, by Hagen Knaf and Franz-Viktor Kuhlmann.
The proof in this paper uses different methods, being inspired by the approach
of Zariski and Abhyankar.
