  We provide all basic equations and concepts required to carry out a general
study on axially symmetric static sources. The Einstein equations and the
conservation equations are written down for a general anisotropic static fluid
endowed with axial symmetry. The structure scalars are calculated and the
inhomogeneity factors are identified. Finally some exact analytical solutions
were found. One of these solutions describes an incompressible spheroid with
isotropic pressure and becomes the well known interior Schwarzschild solution
in the spherically symmetric limit, however it cannot be matched smoothly to
any Weyl exterior metric. Another family of solutions was found that
corresponds to an anisotropic fluid distribution and can in principle be
matched to a Weyl exterior.
