All-electron ab initio Hartree-Fock (HF), multiconfiguration self-consistent-field (CASSCF), and configuration interaction (CI) calculations have been carried out to determine the low-lying electronic states of the Ga2 molecule. Six states, bound relative to the 2P ground-term Ga atoms, have been identified in the CI calculations. The Ga2 molecule has a 3-PI-u electronic ground state, and the next higher lying states are 3-SIGMA-g-, 1 1-SIGMA-g+, 1-PI-u, 1-DELTA-g, and 2 1-SIGMA-g+. The calculated vibrational frequency for the 3-PI-u ground state, 175 cm-1, compares well with the experimental value of 180 cm-1. The six lowest lying electronic states have been rationalized in a simple molecular orbital diagram. On the basis of wave functions determined in valence CI calculations, the oscillator strengths have been computed for selected dipole-allowed transitions. Our calculated transition energies and oscillator strengths compare favorably with the available absorption and emission spectra of Ga2. An approximate treatment of the spin-orbit coupling in the low-lying electronic states of the Ga2 molecule has been carried out. The four lowest lying spin-orbit coupled states, 0u-, 0u+, 1u, 2u, are essentially the split 3-PI-u state. The next higher lying state, 0g+, exhibits a double minimum due to the mixing of the states 3-SIGMA-g- and 1-SIGMA-g+. The dissociation energy of the Ga2 molecule has been determined from the high-temperature mass spectrometric data combined with the experimental vibrational frequency and the spin-orbit coupled electronic states from the present work as D0-degrees = 110.3 +/- 7 kJ mol-1.