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Three different crystal phases of magnesium oxide [B1 (NaCl), B2 (CsCl), and B${8}_{1}$ (inverse NiAs)] are investigated theoretically. An ab initio all-electron linear combination of atomic orbitals Hartree-Fock approximation is adopted; extended basis sets are used which have been variationally optimized in each case. In ordinary conditions, the B${8}_{1}$ and B2 structures result less stable with respect to the rocksalt structure by 0.44 and 1.77 eV, respectively. With increasing pressure, the transition B1\ensuremath{\rightarrow}B2 is estimated to occur around 2.2 Mbar, while it is not excluded that a pressure interval exists around 2 Mbar where the B${8}_{1}$ phase is the most stable of the three structures. Data on the electronic properties of the three phases are provided and discussed: Mulliken populations, charge-density distribution, electron momentum distribution and anisotropy, magnesium core deformation, and band structure.