  A group-theoretical connection between horizontal symmetry $\G$ and fermion
mixing is established, and applied to neutrino mixing. The group-theoretical
approach is consistent with a dynamical theory based on $U(1)\times \G$, but
the dynamical theory can be used to pick out the most stable mixing that purely
group-theoretical considerations cannot. A symmetry common to leptons and
quarks is also discussed. This higher symmetry picks $A_4$ over $S_4$ to be the
preferred symmetry for leptons.
