The spectra of the absorption, luminescence, magnetic circular dichroism (MCD) and magnetic circular polarization of luminescence (MCPL) in the praseodymium yttrium garnet aluminate Pr 3 + :YAG have been studied within the visible and near ultraviolet (UV) spectral range for temperature T=90K and 300K. 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 1 D 2 , 3 P 0 and 3 H 4 multiplets in Pr 3 + :YAG. It has been shown that for Pr 3 + :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 3 H 4 multiplet of the non-Kramers RE Pr 3 + ion. A parameterized Hamiltonian defined to operate within the entire 4f 2 ground electronic configuration of Pr 3 + 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, B q k , 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 18cm - 1 .