The emission and reflection spectra of GaN have been investigated in the intrinsic region and the data have been interpreted in terms of the wurtzite crystal band structure. Three intrinsic exciton transitions have been observed, one associated with each of the valence bands. Exciton excited states associated with the two top valence bands were also observed. The exciton binding energies, the band-gap energies, and the exciton Bohr radii are all reported along with the dielectric constant and the spin-orbit and crystal-field parameters for GaN.