Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies

For space-times with two spacelike isometries, we present infinite hierarch ies of exact solutions of the Einstein and Einstein-Maxwell equations as re presented by their Ernst potentials. This hierarchy contains three arbitrar y rational functions of an auxiliary complex parameter. They are constructe d using the so-called "monodromy transform" approach and our new method for the solution of the linear singular integral equation form of the reduced Einstein equations. The solutions presented, which describe inhomogeneous c osmological models or gravitational and electromagnetic waves and their int eractions, include a number of important known solutions as particular case s.