  We present a first principles study of NMR and spin orbit effects in the
unconventional superconductor Sr2RuO4. We have calculated the uniform magnetic
susceptibility, which agrees rather well with the experiment in amplitude, but,
as in an earlier model result we found the calculated hard axis to be z,
opposite to the experiment. We have also calculated the Knight shifts and the
NMR relaxation rates for all atoms, and again found an overall good agreement,
but important deviations from the experiment in same particular characteristic,
such as the Knight shift anisotropy. Our results suggest that correlations in
Sr2RuO4 lead to underestimations of the orbital effects in density-functional
based calculations. We also argue that the accepted ``experimental'' value for
the relative contribution of orbital polarization in susceptibility, 10-15%, is
also an underestimation. We discuss the puzzling invariance of the the O and Ru
Knight shift across the superconducting transition for all directions of the
applied field. We show that this fact cannot be explained by accidental
cancellations or spin-flip scattering, as it happens in some elemental
superconductors. We also point out that large contribution of the dipole and
orbital hyperfine field into the Knight shifts in Sr2RuO4, combined with the
possibility of an orbital-dependent superconductivity, calls for a revision of
the standard theory of the Knight shift in the superconducting state.
