A theoretical discussion of the theory of Raman scattering by phonons in crystals is given. The hamiltonian is taken as H = H0 + H1 where H0 is: the hamiltonian of the photons, HR ; plus the hamiltonian of the phonons, H L ; plus the electron hamiltonian HE. The interaction term is H1, which is the sum of electron-radiation hamiltonian HER, plus the electron-lattice hamiltonian HEL. Either one particle Bloch basic states, or exciton basic states can be used for HE ; the harmonic approximation is used for HL. Thus : H = HR + HL + HE + HER + HEL. The operators are written in second quantized form. By performing suitable canonical transformations the interaction term is eliminated, in lowest order. The remaining hamiltonian can then be transformed using quasi particle creation-destruction operators. Raman scattering can then be calculated using first order time dependent perturbation theory, taking the appropriate higher order commutators as the (transformed) perturbing hamiltonian, and evaluating certain matrix elements. More simply (in lower order) the product eigenstates of H0 can be used to describe Raman scattering, taking the appropriate matrix-element of the transformed, perturbing, hamiltonian. Comparison can then be made with the results of Loudon [1]. This method enables us to deal also with the case in which HEL is larger than HER. For example, if HEL were a first order perturbation, while HER was second order (as perhaps in an ionic crystal such as CaF2 where the Frohlich electron-lattice interaction may be relevant). Differences between this case, and the former case in which HEL and HER are of same order will be discussed. Other applications of this method will be presented for example spin-flip (magnetic dipole) Raman-lattice scattering will be proposed as a novel process in heavy ion ionic crystals.