Altermagnetism is the name given to compensated weakly spin-orbit coupled magnetic materials with anisotropic momentum space spin-splitting in their band structures. In this talk, I introduce the central ideas that lead to altermagnetic spin-splittings and in particular the concept of spin symmetries. It is possible to write down Landau theories for these magnets and I will describe how to do this and some of the many consequences for experiment. Time allowing I shall also describe some of the broader implications of spin symmetries in condensed matter.