We shall first study the composite motion of a particle. It will be shown that the description of the absolute motion of a particle can be related with that of simpler motions such as the relative motion and a number of bulk (transport) ones. The results obtained for the composite motion of a particle are applied to examine the composition of motion of a rigid body. We shall consider the composition of translational motions of a rigid body and rotational ones, including a couple of rotations.