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 deeper insights into the galaxy formation and large-scale matter distribution as well.
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