The asymptotical solution of nonlinear equations by means of Power Geometry

We give a simple presentation of main consepts and algorithms of Power Geometry: the support and the polyhedron of an equation, faces and truncations of the equation, power transformations and logarithmic transformations of the equation. The third Painleve's equation is used for examples. We give also a survey of some applications of Power Geometry: for a study of motions of a rigid body with a fixed point, in the theory of the boundary layer on a needle, in the equation of oscillations of a satellite.