The theory of oscillations of solar neutrinos is developed as it applies to the electron-recoil spectrum in neutrino-electron scattering. The spectral information obtained by such measurements (as opposed to counting total event rates) is crucial for allowing observation of neutrino oscillations for masses down to 500 neV. In this regard, the effects of different masses and mixing angles, as well as such subtleties as thermal and pressure broadening, finite solar-core size, and variable indices of refraction are investigated.