Symmetries are a powerful organizing tool that simplify and constrain our models to study the world around us that exhibits these symmetries. To understand symmetries we need to understand group theory. This project combines the maths of group theory and the physics of the standard model of particle physics that describes the interactions of fundamental particles around us. Building on the group theory that you studied in Geometry of Mathematical Physics, you will deepen your understanding of group theory and representations of groups, and apply it to the study of gauge theories. Using this knowledge and the companion module of Advanced Quantum Theory, you will study Goldstone's theorem for spontaneously broken symmetries, and the Higgs mechanism, that explains how particles get a mass in the standard model.