The electronic structure of the cubic and (high pressure) hexagonal phases of Eu₂O₃ have been investigated by means of full potential linearized augmented plan wave calculations, within the LDA + U method. A full structural relaxation was performed for both phases, and the transition pressure was determined. The band structure shows the correct insulating character with gap values comparable to the experimental ones. The contact charge density was also calculated for Eu₂O₃ (and other Eu compounds) and found to be in good agreement with experimental values. For the cubic phase, the comparison between ferromagnetic and antiferromagnetic calculations show that the exchange interaction is very weak and is therefore expected to have a negligible effect on the magnetic susceptibility. The claculations performed for the high pressure hexagonal phase, on the other hand, show that there is an antiferromagnetic exchange interaction between nearest-neighbor Eu ions, which should have a sizable effect on the susceptibility. Our results allow us to evaluate the existing theories.