Image-tube photographs taken through narrow-band interference filters have been used to obtain monochromatic surface brightnesses of the Ring Nebula (NGC 6720) in the strongest emission lines of H I, He I, He II, [N II], [O I], [O II], [O III], and [S II]. These data have been used to analyze the spatial distribution of the various ionized species within the nebula. The bulk of the observed emission is shown to arise from a network of neutral filaments whose inner surfaces are ionized by the incident stellar radiation. The filamentary network is embedded in a low-density, high-temperature medium which is the source of most of the observed high-excitation lines. The ionization structure of several prominent filaments is examined in detail and comparisons are made to recent ionization structure calculations.