The Standard Model (SM) of particle physics has been supported by experiment for four decades. Ongoing high energy experiments in the LHC at CERN and the Tevatron at Fermilab are pursuing the last missing element of experimental support, the discovery and measurement of the Higgs boson. Nevertheless, at the edge of the experimental program hints of possible divergence from theory have appeared, especially in the area of flavour physics, the phenomenology (interactions and mixings) of the six types or flavours of quarks and leptons. Furthermore, the inability of the Standard Model to provide an explanation for certain phenomena such as the amount of matter-antimatterasymmetry in the Universe, or the hierarchical values of the masses and couplings strengths of fermions, has led most physicists to believe that the Standard Model is only an effective theory, that is, an approximation to an yet undiscovered, morefundamental theory. So it is that even if the existence and characteristics of the Standard Model Higgs boson are experimentally verified (recent reports are not promising), experiments at hitherto unattained energies and levels of precision will continue to be required to elucidate thephenomena that are beyond the Standard Model(BSM).Currently there is a large experimental program providing flavour physics data in Europe, USA, and Asia: BaBar, Belle, Tevatron, CLEO; the newer LHCb and NA62 at CERN, BES-III in Beijing, and KLOE-2 in Frascati; and the forthcoming Belle-II and J-PARC in Japan. The ever-increasing precision of data from such experiments requires a commensurate increase in the accuracy of the predictions derived from theory. Development of new, as well as continued refinement of existing, lattice QCD methods is required to attain theoretical predictions with such levels of precision. The research program described in this proposal is focused directly on this need.