Calculations of cross sections for elastic scattering, rotational excitation, and vibrational excitation of ground state N2 by electrons with impact energies of 10 and 50 eV have been performed using realistic static-exchange-plus-polarization interaction potentials, rotational close coupling, and the vibrational sudden approximation. The effect of vibrational averaging on the elastic scattering is found to be small. The calculated integral cross sections for pure elastic scattering and for pure rotational (summed over j′≠0), pure vibrational (j′=0,v′=1 and 2), and mixed rotational-vibrational (summed over j′≠0 for v′=1 and 2) excitation are 34.4, 18.6, 2.70×10-2, and 4.13×10-2 a02, respectively, at 10 eV and 19.4, 11.7, 1.28×10-2, and 6.92×10-2 a 02, respectively, at 50 eV. The sum of the differential cross sections for pure vibrational and mixed rotational-vibrational excitation for v=0→v′=1 can be compared to experiment and agreement is good at both energies except for scattering angles θ≤130°. The pure rotational excitation differential cross section has not been resolved experimentally but we predict that it is dominated by j′=2 at 10 eV and for θ≤130° at 50 eV and j′=4 for larger θ at 50 eV. The calculated state-to-state cross sections are also compared to results calculated by the polarized Born approximation with simplified model potentials based on the long-range forces.