The collapse and subsequent explosion of stars in supernova events play a fundamental role in producing and distributing throughout the Universe most of the elements heavier than hydrogen and helium. This project involves a theoretical investigation of the supernova core collapse process. One- two- and three-dimensional approaches are being taken towards constructing an extensive grid of numerical models for the collapse phase of the supernova event. The goal of this effort is to determine the relative effects of spherical symmetry, neutrino transport, axial symmetry and convection on the models and their agreement with the observed characteristics of supernova events. The one- and two-dimensional simulations utilize existing neutrino transport code. Additional 3-D code is being developed to investigate the effects of convection on the hydrodynamic properties of supernova.