This Element is a concise, high-level introduction to the philosophy of physical symmetry. It begins with the notion of 'physical representation' (the kind of empirical representation of nature that we effect in doing physics), and then lays out the historically and conceptually central case of physical symmetry that frequently falls under the rubric of 'the Relativity Principle,' or 'Galileo's Ship.' This material is then used as a point of departure to explore the key hermeneutic challenge concerning physical symmetry in the past century, namely understanding the physical significance of the notion of 'local' gauge symmetry. The approach taken stresses both the continuity with historically important themes such as the Relativity Principle, as well as novel insights earned by working with contemporary representational media such as the covariant phase space formalism.