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We analyse a supersymmetric string-inspired model of all fermion masses andmixing angles based on the Pati-Salam $SU(4)\times SU(2)_L \times SU(2)_R$gauge group supplemented by a $U(1)_X$ flavour symmetry.  The model involves third family Yukawa unification and predicts the top massand the ratio of the vacuum expectation values $\tan \beta$.  The model also provides a successful description of the CKM matrix andpredicts the masses of the down and strange quarks.  However our main focus is on the neutrino masses and MNS mixing angles, andwe show how the recent atmospheric neutrino mixing observed bySuper-Kamiokande, and the MSW solution to the solar neutrino problem lead toimportant information about the flavour structure of the model near the stringscale.  We show how single right-handed neutrino dominance may be implemented by theuse of ``Clebsch zeros'', leading to the LMA MSW solution, corresponding tobi-maximal mixing. The LOW MSW and SMA MSW solutions are also discussed.Comment: 53 pages, Late

Neutrino masses and mixing angles in a realistic string-inspired model