We present a theoretical study of the cyclooctatetraene (COT) molecule. Seven COT structures are located on the singlet ground state potential energy surface. Four of them, which present D-2d (tub), C-s (bicyclo[4.2.0]octa-2,4,7-triene or BOT), C-2h (chair) and D-4 (crown) symmetries are stable species, and the other three are transition state structures showing C-s, D-4h and D-8h symmetry. We discuss the symmetry of wave functions for these stationary points. Geometries, energies, and harmonic vibrational frequencies of these structures, and energy gaps between singlet-triplet states and low-lying singlets an presented. For the planar D-4h and D-8h structures, Jahn-Teller and tunneling effects have also been discussed. Ring inversion, bond shifting and valence isomerization reactive channels from the tub COT conformer are discussed from the point of view of the corresponding transition state structures. Where possible, in order to lend support to this theoretical information comparisons with recent transition state spectroscopy data are made.