The self-propulsion of a generally deformable body at low-Reynolds-number conditions is discussed. The translational and rotational velocities of the body relative to an inertial reference system are presented as surface quadratures using a Lagrangian ‘body-fixed’ shape description. The power dissipated into the fluid is obtained as a quadratic functional of the surface deformation rate. For symmetric strokes, the net displacement obtained by the execution of a single deformation cycle is provided by a functional of the intrinsic swimmer shape and its time derivative.