In this dissertation we develop a theoretical framework in the context of perturbative QuantumChromoDynamics (pQCD) for studying non-forward scattering processes. In particular, we investigate a non-forward unequal mass virtual Compton scattering amplitude by performing the general operator product expansion (OPE) and the formal renormalization group (RG) analysis. We discuss the general tensorial decomposition of the amplitude to obtain the invariant amplitudes in the non-forward kinematic region. We study the OPE to identify the relevant operators and their reduced matrix elements, as well as the corresponding Wilson coefficients. We find that the OPE now should be done in double moments with new moment variables. There are in the expansion new sets of leading twist operators which have overall derivatives. They mix under renormalization in a well-defined way. We compute the evolution kernels from which the anomalous dimensions for these operators can be extracted. We also obtain explicitly the lowest order Wilson coefficients. In the high energy limit we find the explicit form of the dominantly contributing anomalous dimensions. We are then able to solve the resulting renormalization group equations (RGE) and give a prediction of the high energy behavior of the invariant amplitudes. We find that it is the same as is indicated by the conventional double leading logarithmic analysis.