  We construct algebraically closed fields containing an algebraic closure of
the field of power series in several variables over a characteristic zero
field. Each of these fields depends on the choice of an Abhyankar valuation and
are constructed via the Newton-Puiseux method. Then we study more carefully the
case of monomial valuations and we give a result generalizing the
Abhyankar-Jung Theorem for monic polynomials whose discriminant is weighted
homogeneous.
