High-level ab initio calculations of the ground and several excited-state adiabatic potential surfaces of the NaFH system are reported. These calculations were performed by multireference configuration interaction on a large grid of geometries which allowed them to be used for constructing an accurate analytic representation of the NaFH potential surfaces. For the ground and first excited states, using a genetic algorithm, an analytic 2X2 matrix fit was obtained corresponding to a diabatic representation. The off-diagonal coupling was obtained by fitting the energy gap between the surfaces in the region of their avoided crossing, and the diagonal elements were then fit to reproduce the ab initio adiabatic energy at 1530 points. The full fit was used to locate the barrier and the van der Waals well on the ground-state potential surface, the exciplex on the first-excited-state potential surface, and the minimum energy path for the ground-state Na+HF-->NaF+H reaction. Additional calculations on the van der Waals and saddle point regions were carried out by a variety of ab initio methods as a check on accuracy. Major topological features of the potential energy surfaces representing higher-than-first excited states were examined.