When the atoms of simple metals condense from the gas phase to give a solid, the valence electron wavefunctions are strongly modified by their overlap. At first sight this strong overlap might be expected to produce a complex situation, difficult to treat quantitatively. Yet the simple metals are perhaps the best understood of all solids and the reason is that the electron wavefunctions are plane-wave-like to a first approximation and deviations can be treated by perturbation theory.