  We present a general perturbative effective field theory (EFT) description of
galaxy shape correlations, which are commonly known as intrinsic alignments.
This rigorous approach extends current analytical modelling strategies in that
it only relies on the equivalence principle. We present our results in terms of
three-dimensional statistics for two- and three-point functions of both galaxy
shapes and number counts. In case of the two-point function, we recover the
well-known linear alignment result at leading order, but also present the full
next-to-leading order expressions. In case of the three-point function we
present leading order results for all the auto- and cross-correlations of
galaxy shapes and densities. We use a spherical tensor basis to decompose the
tensor perturbations in different helicity modes, which allows us to make use
of isotropy and parity properties in the correlators. Combined with the results
on projection presented in a forthcoming companion paper, our framework is
directly applicable to accounting for intrinsic alignment contamination in weak
lensing surveys, and to extracting cosmological information from intrinsic
alignments.
