  We present an SU(4) model of high-$T_c$ superconductivity. One dynamical
symmetry of this model corresponds to the previously proposed SO(5) model for
unification of superconductivity and antiferromagnetism, but there are two
additional dynamical symmetries: SO(4), associated with antiferromagnetic order
and SU(2), associated with a D-wave pairing condensate. These provide a 3-phase
microscopic model of high-$T_c$ superconductivity and permit a clear
understanding of the role played by the SO(5) symmetry.
