The resolution of curves singularities over C has long been known and has many proofs. One of them consists in using the Newton-Puiseux theorem to obtain the local uniformization of a valuation centered on the starting ring. This theorem provides a puiseux expansion to parametrize the branches of the curve and a set of polynomials describing completely the valuation. In this thesis we generalize this method using key polynomials indexed by a well-ordered set which become coordinates after blowings up. Our first result provides an effective generalization of the Newton-Puiseux theorem for valuation of rank 1 centered on a complete regular local ring and integral relations on the truncation of the series. In the next chapter, we show that there is no limit key polynomials in characteristic zero and we propose a method for the local uniformization of quasi-excellent schemes. This method consists in resolving the singularities of the implicit prime ideal generated by a polynomial and monomializing key polynomials. Finally, in positive or mixed characteristic, we show that, under certain conditions, to obtain the local uniformization it is sufficient to monomialize the first limit key polynomial.
