This Element explores what it means for two theories in physics to be equivalent (or inequivalent), and what lessons can be drawn about their structure as a result. It does so through a twofold approach. On the one hand, it provides a synoptic overview of the logical tools that have been employed in recent philosophy of physics to explore these topics: definition, translation, Ramsey sentences, and category theory. On the other, it provides a detailed case study of how these ideas may be applied to understand the dynamical and spatiotemporal structure of Newtonian mechanics - in particular, in light of the symmetries of Newtonian theory. In so doing, it brings together a great deal of exciting recent work in the literature, and is sure to be a valuable companion for all those interested in these topics.

Introduction; 1. Definitions; 2. Translation; 3. Ramsey sentences; 4. Categories of theories; 5. Newtonian mechanics; 6. Symmetry; 7. Galilean spacetime; 8. Conclusion; References.