Large Neutrino Mixings and Other Key Issues in Supersymmetric SU(4)$_c \times $ SU(2)$_{\rm L} \times$ SU(2)$_{\rm R}

We try to gain an understanding of the recent Superkamiokande data on neutrino oscillations and several other important phenomenological issues within the framework of supersymmetric $SU(4)_c \times SU(2)_L \times SU(2)_R$ ($\equiv G_{422}$). By supplementing $G_{422}$ with a $U(1)$-${\cal R}$ symmetry, we can provide an explanation of the magnitude $M_G$ ($\sim 10^{16}$~GeV) of the $G_{422}$- symmetry breaking scale, resolve the MSSM $\mu $ problem, and understand why proton decay has not been seen ($\tau_p \gg 10^{34}$~yr). The family dependent ${\cal R}$ - symmetry also helps provide an explanation of the charged fermion mass hierarchies as well as the magnitudes of the CKM matrix elements. Several additional heavy states in the mass range $10^4-10^7$~GeV are predicted, and the MSSM parameter $\tan \beta $ turns out to be of order unity. The resolution of the solar neutrino puzzle is via vacuum oscillation and necessarily requires a sterile neutrino $\nu_s$ which, thanks to the ${\cal R}$ - symmetry , has a tiny mass. The atmospheric neutrino problem is explained through $\nu_{\mu}-\nu_{\tau }$ mixing. Large mixing angles are shown to arise naturally in the neutrino sector.