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The /?-matrix method has been used to study the scattering of electrons by oxygen molecules for impact energies in the range from threshold to 15 eV. Electronic excitation cross sections for transitions to the fl'Ag, ^'S/, and "6 eV" states of oxygen are presented. Important contributions from a ^n^ resonance, in addition to the well-known ^Flg resonance, are found to significantly modify previous theoretical predictions. Integral elastic scattering cross sections are also obtained for the first time for a complicated open-shell system using an ab initio method. PACS numbers: 34.80. Bm Detailed information about collisions between lowenergy electrons and oxygen molecules is required in studies of the physics of planetary atmospheres, gaseous discharges, and both astrophysical and laboratory plasmas. The collision has been extensively studied experimentally [ll but there have been few theoretical studies. The electronic excitation cross sections of the a and b excited states were first calculated by Noble and Burke [2] using the /^-matrix method [3]. Only the three lowest electronic states of the target molecule were taken into account. The results confirmed the dominant role of the resonant ^Wg symmetry and were in reasonable agreement with experiment. More recently, Teillet-Billy, Malegat, and Gauyacq [4], using multichannel effectiverange theory (ERT), have demonstrated the multichannel nature of the shape resonance in this symmetry and the necessity of including all electronic states of the target which are parents of the resonance in accurate collision calculations.In this Letter we present new results for the electronic excitation from the ground state demonstrating that contributions from other scattering symmetries are important and significantly modify previous theoretical estimates of the cross sections. These results are obtained using the /^-matrix method with a model including nine electronic states of the target molecule and configuration interaction (CI) representations of the target wave functions. We also obtain estimates of the elastic scattering cross section for impact energies up to 15 eV. This work represents one of the first ab initio calculations of electron scattering from an open-shell molecule.The /^-matrix method has now been successfully applied for more than a decade in studies of collisions between photons, electrons or positrons, and diatomic molecules. The essential techniques have already been described [5] and need not be repeated here. It is suflRcient to note that the complete electrostatic interaction between the target and the incident electron is taken into account within a spherical region of configuration space defined by values of the radial coordinate of the incident electron being less than some predetermined value chosen