  Emphasizing the contribution of Professor Roger A Cowley, FRS to the Theory of Raman Scattering from crystals, the development of the Theory of Raman cattering since 1928 has been briefly discussed. Some experimental studies of Strontium Titanate using Inelastic Neutron Scattering, Raman Scattering, Electro- paramagnetic resonance measurement and X-ray & Gamma Ray techniques has been briefly discussed. Using Schwabl's semi-phenomenological theory for the soft mode and central peak, we have developed (a) a one-phonon Green's function exhibiting the three peaked structure and (b) a two phonon Green's function involving one hard mode under damped quasiharmonic phonon and one three peaked soft-mode phonon. We have developed the pre-cursor order induced Raman scattering near the displacive phase transition in terms of Green's functions. Using Group Theory, we have predicted the Raman-active modes in Strontium Titanate contributing to Critical Raman Scattering near hard-mode frequencies above and below critical temperature. We have calculated the Critical Integrated Raman Scattering Intensity and the Two-phonon Background Raman Scattering Intensity near hard-mode frequencies above and below the critical temperature. The results show the same trends as observed in some of the experimental observations. 
Critical Integrated Raman Scattering Intensity near the cubic-tetragonal   phase transition in Strontium Titanate