  A monodromy transform approach, presented in this communication, provides a
general base for solution of space-time symmetry reductions of Einstein
equations in all known integrable cases, which include vacuum, electrovacuum,
massless Weyl spinor field and stiff matter fluid, as well as some string
theory induced gravity models. It was found a special finite set of functional
parameters, defined as the monodromy data for the fundamental solution of
associated spectral problem. Similarly to the scattering data in the inverse
scattering transform, these monodromy data can be used for characterization of
any local solution of the field equations. A "direct" and "inverse" problems of
such monodromy transform admit unambiguous solutions. For the linear singular
integral equation with a scalar (i.e. non-matrix) kernel, which solves the
inverse problem of this monodromy transform, an equivalent regularization -- a
Fredholm linear integral equation of the second kind is constrcuted in several
convenient forms. For arbitrary choice of the monodromy data a simple iterative
method leads to an effective construction of the solution in terms of
homogeneously convergent functional series.
