This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project objectives were (1) to develop highly optimized codes for the simulation of lattice Quantum Chromodynamics (QCD) on the Connection Machine CM-5, (2) to use these codes to carry out a comprehensive analysis of Standard Model phenomenology using a large statistical sample, and (3) to combine the results of numerical simulations with experimental data to estimate the unknown parameters of the Standard Model. We were successful in achieving all these goals. Our highly optimized codes were used to debug both the hardware and software of the CM-5. We carried out a comprehensive study of the hadron spectrum, decay constants for mesons, semi- leptonic form factors, form-factors for the rare decay B {r_arrow} K{sup *} {gamma}, {pi}-{pi} scattering amplitude, and matrix elements of a variety of 4-fermion weak operators. From these observables we were able to predict the masses of light quarks, m{sub u} + m{sub d} and m{sub s}, matrix elements of the Cabibbo-Kobayashi-Maskawa mixing matrix, and the CP violating parameters {epsilon} and {epsilon}{prime}. Our new estimates of light-quark masses are roughly half of commonly believed values, and we predict a much larger value for {epsilon}{prime}/{epsilon}, which will be tested experimentally over the next few years. 15 refs.