This thesis reports measurements of absolute differential cross sections for elastic scattering of atomic oxygen at 0.5- and 1.5-keV laboratory energies. Measurements for targets of He, Ne, Ar, Kr, Xe, H\sb2, N\sb2, O\sb2, CO, CO\sb2, H\sb2O, CH\sb4, CF\sb4, SF\sb6, SO\sb2, and NH\sb3 are performed over a laboratory angular range of 0.2 to 5.0 degrees. Using a partial wave analysis, the cross sections for several targets are inverted and estimates of model interaction potentials are made. These potentials are then used to predict the elastic scattering cross sections at a laboratory energy of 100 eV.