Consequences of Approximate $S_3$ Symmetry of the Neutrino Mass Matrix

Assuming that the neutrino mass matrix is dominated by a term with the permutation symmetry $S_3$ it is possible to explain neutrino data only if the masses are quasi-degenerate. A sub-dominant term with an approximate $\mu -\tau$ symmetry leads to an approximate tri-bimaximal form. Experimental consequences are discussed.