  We present a theoretical study of galaxy spin correlation statistics, with
detailed technical derivations. We also find an expression for the spin-density
cross-correlation, and apply that to the Tully galaxy catalog. The
observational results appear qualitatively consistent with the theoretical
predictions, yet the error bars are still large. However, we expect that
currently ongoing large surveys such as the Sloan Digital Sky survey (SDSS)
will enable us to make a precision measurement of these correlation statistics
in the near future. These intrinsic galaxy alignments are expected to dominate
over the weak lensing signal in SDSS, and we present the detailed algorithms
for the density reconstruction for this case.
  These observables are tracers of the galaxy-gravity interaction, which may
provide us deeper insights into the galaxy formation and large scale matter
distribution as well.
