The detailed calculation of the electronic structure of the spin-Peierls CuGeO 3 crystal was made within the limits of a spin-unrestricted Hartree-Fock method, simplified by means of a complete neglecting of difference overlap approximation. The crystal lattice polarization due to one-particle excitations has been also taken into account to improve the description of the insulating gap and vacant crystal states. This calculation has given the local magnetic moments, ionic charges, crystal valences, and partial densities of states. The correct insulating gap value of about 3 eV was obtained. It was shown that this gap corresponds to the charge transfer from 2 p oxygen to 3d copper atomic orbitals. The nature of several first optical transitions was considered. We have compared our results with those results which have been given by local-density approximation-linear augmented plane-wave and local-density approximation-linear muffin-tin orbital methods. We considered the eight different Néel magnetic states using the expansion of the unit cell. We calculated the total energies of this states and employed them to obtain the values of exchange integrals J c ϭ11.5Ϯ0.3 meV, J b ϭ0.45 Ϯ0.20 meV, J a ϭ0.05Ϯ0.05 meV, which are in good agreement with experimental data on magnetic neutron scattering and x-ray diffraction and antiferromagnetic EPR for this compound. We discuss possible schemes of exchange interactions between spins localized on neighboring Cu atoms. The electronic structure of the same Néel states of CuGeO 3 in a dimerized configuration was determined. We did not find any changes of the band structure for all considered Néel spin states in the dimerization. The dependence of J c as a function of Cu-Cu distance along the c axis was obtained, which enabled us to determine the alternation parameter ␦ϭ0.007 in the linearized model of the dimerized state ͓J c 1,2 ϭJ c (1Ϯ␦)͔. The values of ⌬ SP (␦ϭ0.007)ϭ0.43 meV and ⌬E 0 (␦ϭ0.007)ϭ5ϫ10 Ϫ3 meV were calculated in terms of Bulaevskii's Hartree-Fock analysis.