Solving the polynomial equations by algorithms of power geometry

New methods for computation of solutions of an algebraic equation of three variables near a critical point are proposed. These methods are: Newton polyhedron, power transformations, new versions of the implicit function theorem and uniformization of a planar algebraic curve. We begin from a survey of the new methods of computation of solutions of an algebraic equation of one and of two variables by means of the Hadamard polygon and Hadamard polyhedron. That approach works for differential equations (ordinary and partial) as well.