Prediction of the atomic geometry of metal surfaces demands a detailed knowledge of their electronic structure. In this thesis we have used an ab initio tight binding method to perform calculations on a variety of materials in which d electrons make an important contribution to the bonding. The non-hermitian formulation which we use is directly based on the local electronic structure concept in which an atom sees the solid around it only as a perturbation to its free state. Calculation of bulk and surface states of W, Mo, Cu, Ag, Pd, TiN, ZrN, TiC and ZrC using this method gives results which are in reasonable agreement with published experimental work. In order to carry out the total energy calculations needed to predict displacements of surface atoms an empirical repulsive interaction must be added to the energy of the one-electron states. The parameters of this interaction are obtained by constraining the calculated total energy to reproduce the lattice constant and bulk modulus of the infinite solid correctly. The relaxations for W and Mo surfaces which this method predicts axe comparable with those observed experimentally. This same parametrisation indicates that the well known reconstructions of the W and Mo {001} surfaces do not lead to a reduction in total energy.