One- and two-particle effects in the electronic and optical spectra of the fluoride compound BaF2 are determined using density functional theory and a many-body perturbation scheme. A wide energy range has been considered, including the visible and all the ultraviolet region. The GW approximation for the electronic self-energy has been used to tackle the one-particle excitations problem, enabling us to determine the electronic energy bands and densities of states of this fluoride. For the optical properties, the two-particle effects calculated with the Bethe-Salpeter scheme turn out to play a fundamental role. A bound exciton positioned at about 1.5 eV below the one-particle gap is forecasted. The optical absorption and the electron energy loss spectra together with other optical functions are in good agreement with the experimental results up to 15 eV. In fact, for this part of the spectrum a self-consistent one-particle scheme along with the Bethe-Salpeter approach produces notable results. Less satisfactory results for the higher energy region in the spectra have been produced with the proposed method. Possible causes of these discrepancies are fully discussed.