For the last twenty years Mike McHenry and I have taught courses on magnetic materials at Carnegie Mellon University. Our shared fascination with symmetry principles has colored the way we teach these classes. In this lecture various, often overlooked, roles played by the symmetry of magnetic materials will be explored. Topics will include the axial symmetry of the magnetic moment, magnetic crystal structure, the paramagnetic to ferromagnetic transition according to the Landau criteria, the anisotropic Curie temperature, piezomagnetism / magnetostriction and the formation of magnetic domains. If time permits other tensor properties will be presented and discussed in the light of magnetic symmetry.