If Γ is an irreducible representation of a group 𝒢, and ℋ is a subgroup of 𝒢, then Γ furnishes a representation of ℋ which is, in general, reducible, and the branching rules specify which irreducible representations of ℋ occur in the decomposition of this representation. Branching rules are derived for various choices of 𝒢 and ℋ, including most possibilities that have been discussed as higher symmetry groups.