We report anisotropic spectra of 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA) in the optical energy range 1.5-3.7 eV, measured at room temperature by spectroscopic ellipsometry. The results were obtained on single crystals of a-PTCDA grown by temperature gradient sublimation. Spectra were measured at highly symmetric positions of the plane of incidence relative to the sample crystallographic axes and are presented as pseudo-values of refractive index hni and extinction coefficient hki, which reflect a very large anisotropy of these optical functions. The spectroscopic properties of the excited states in the molecular plane (1 0 2) are analyzed; in particular, we identify clear Davydov splittings proving the formation of coherent excitons in the crystal. Out-of-plane, we observe a relatively narrow absorption peak at $2.9 eV that is ascribed to a charge-transfer transition. Ó