The spectra of the absorption, luminescence, magnetic circular dichroism (MCD) and magnetic circular polarization of luminescence (MCPL) in the praseodymium yttrium garnet aluminate Pr3+:YAG have been studied within the visible and near ultraviolet (UV) spectral range for temperature T=90 K and 300 K. Analysis of the spectral and the temperature dependences of the magnetooptical and optical spectra has made it possible to identify the optical 4f→4f transitions occurring between the Stark sublevels of the 1D2, 3P0 and 3H4 multiplets in Pr3+:YAG. It has been shown that for Pr3+:YAG in the MCD within the UV spectral range for the absorption bands due to allowed 4f→5d transitions, and also in the MCPL for the luminescence bands, respectively, due to forbidden 4f→4f transitions within the visible spectral range, a significant role is being played by the effect of quantum mechanical “mixing” of the states of the three lowest energy Stark singlets of the ground state 3H4 multiplet of the non-Kramers RE Pr3+ ion. A parameterized Hamiltonian defined to operate within the entire 4f2 ground electronic configuration of Pr3+ was used to model the experimental Stark levels, their irreducible representations (irreps) and wave functions. The crystal-field parameters were determined through use of a Monte-Carlo method in which nine independent crystal-field parameters, View the MathML source, were given random starting values and optimized using standard least-squares fitting between calculated and experimental levels. The final fitting standard deviation between 61 calculated to experimental Stark levels is 18 cm−1.