  Using invariant transformations of the five-dimensional Kaluza-Klein (KK)
field equations, we find a series of formulae to derive axial symmetric
stationary exact solutions of the KK theory starting from static ones. The
procedure presented in this work allows to derive new exact solutions up to
very simple integrations. Among other results, we find exact rotating solutions
containing magnetic monopoles, dipoles, quadripoles, etc., coupled to scalar
and to gravitational multipole fields.
