Backlund transformations of axially symmetric stationary gravitational fields

A generation theorem for solutions of Einstein's equations is presented. It consists mainly of algebraic steps. With its aid, one obtained from an 'old' solution (e.g. from the Minkowski space) 'new' solutions with an arbitrary number of constants. The method of repeated application of potential and coordinate transformations considered by Geroch (1972) and Kinnerley (1977) is included.