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.
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