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In spite of the several published cross section sets for the oxygen molecule, some processes in electron collisions with O2 are still under discussion. For example, available experimental data on excitation of O2(b1Σg+) state requires that, in known cross section sets, all higher states lead to excitation of O2(b1Σg+). This is problematic assumption due to the existence of dissociation to ground state atoms. There is a discrepancy between the data about total inelastic losses of electron and sum of the cross sections of the known processes. There is lack of information about near threshold behavior of O2 dissociation cross section, which is very important for plasma processing application of oxygen containing plasma. In this work the review of available experimental and theoretical data concerning these issues is presented. On the base of this review and numerical calculations the self-consisted cross section set is constructed which satisfy the current status of known electron collision processes in oxygen. The electron state excitation cross section with threshold higher than ionization threshold is introduced. The theoretical basis for existence of this cross section is presented. The new cross sections for oxygen dissociation are presented and discussed.