This thesis treats the coherent interaction of light quantum with a crystal, taking proper account of the mutual interactions of the individual scatterers. Of particular interest is the case of resonant scattering. Using the Feynman approach to quantum electrodynamics, we first develop the general ideas with one- and two-particle systems. The major results are then presented in sections V and VI. [see PDF for formulas] In section V we derive a general quantum expression governing the coherent optical properties of an N particle system: In section VI we use these results to treat resonant optics. It is found that at certain well defined frequencies and angles, the interactions among the resonators can lead to a greatly enhanced coherent width, and therefore to suppression of incoherent processes such as inelastic scattering and absorption. It will be shown that for certain conditions, this width enhancement causes anomolously high transmission or reflection.