Modern physics is one of the most exciting subjects studied by humanity, but popular books on the subject usually either over-simplify their content or assume prior knowledge of mathematical theory. Worlds of Motion attempts to cross this bridge by tackling the mathematics in an accessible way, introducing each equation step-by-step and justifying why it is necessary. The book begins with an extended discussion of classical mechanics and then moves on to relativity theory and quantum mechanics, covering all the main principles of modern physics. It covers a huge range of topics in physics, astronomy and pure mathematics to give the reader a greater understanding of the universe. In particular, we treat mathematics as something which is intrinsically exciting in itself and not something to be feared. The book includes entertaining treatments of symmetry groups and topology based in popular culture.