  We develop a general hydrodynamic theory describing a system of interacting
actively propelling particles of arbitrary shape suspended in a viscous fluid.
We model the active part of the particle motion using a slip velocity
prescribed on the otherwise rigid particle surfaces. We introduce the general
framework for particle rotations and translations by applying the Lorentz
reciprocal theorem for a collection of mobile particles with arbitrary surface
slip. We then develop an approximate theory applicable to widely separated
spheres, including hydrodynamic interactions up to the level of force
quadrupoles. We apply our theory to a general example involving a prescribed
slip velocity, and a specific case concerning the autonomous motion of
chemically active particles moving by diffusiophoresis due to self-generated
chemical gradients.
