The angular velocity vector, indicating the rate of change of the orientation of a rigid body in space, is introduced. The expression for the velocities of the various body points during a motion is derived, and the properties of the velocity field are examined. The rule for the differentiation of a vector, specified by its components relative to a rotating frame, is obtained and explained. Next, we consider the relative motion of rigid bodies. Finally, we arrive at the expressions for the velocity and acceleration of a particle in motion relative to the rigid body. Examples having increasing complexity are presented.