  In this paper, the problem of finding an axisymmetric stationary spacetime
from a specified set of multipole moments, is studied. The condition on the
multipole moments, for existence of a solution, is formulated as a convergence
condition on a power series formed from the multipole moments. The methods in
this paper can also be used to give approximate solutions to any order as well
as estimates on each term of the resulting power series.
