We enter the world of three dimensions gently by considering particles. These just have mass, without any moments of inertia of a solid body. We see that vector functions of position can be differentiated, to give vector velocities and accelerations. We define frames of reference and see how the motion of a particle in a rotating frame can be represented in ‘world axes’. Generalised coordinates are mentioned, though a more rigorous mathematical treatment is to be found in an appendix at the end of the book.