  We present a method for generating exact solutions of Einstein equations in
vacuum using harmonic maps, when the spacetime possesses two commutating
Killing vectors. This method consists in writing the axisymmetric stationry
Einstein equations in vacuum as a harmonic map which belongs to the group
SL(2,R), and decomposing it in its harmonic "submaps". This method provides a
natural classification of the solutions in classes (Weil's class, Lewis' class
etc).
