The electron-deficient diatomic boron molecule has long puzzled scientists. As yet, the complete set of bound vibrational energy levels is far from being known, experimentally as well as theoretically. In the present ab initio study, all rotational-vibrational levels of the X (3)Sigma(-)(g) ground state are determined up to the dissociation limit with near-spectroscopic accuracy (<10 cm(-1)). Two complete sets of bound vibrational levels for the B-11(2) and B-11-B-10 isotopomers, containing 38 and 37 levels, respectively, are reported. The results are based on a highly accurate potential energy curve, which also includes relativistic effects. The calculated set of all vibrational levels of the B-11(2) isotopomer is compared with the few results derived from experiment [Bredohl, H.; Dubois, I.; Nzohabonayo, P. J. Mol. Spectrosc. 1982, 93, 281; Bredohl, H.; Dubois, I.; Melen, F. J. Mol. Spectrosc. 1987, 121, 128]. Theory agrees with experiment within 4.5 cm(-1) on average for the four vibrational level spacings that are so far known empirically. In addition, the present theoretical analysis suggests, however, that the transitions from higher electronic states to the ground state vibrational levels nu = 12-15 deserve to be reanalyzed. Whereas previous experimental investigators considered them to originate from the nu' = 0 vibrational level of the upper state (2)(3)Sigma(-)(u), the present results make it likely that these transitions originate from a different upper state, namely the nu' = 16 or the nu' = 17 vibrational level of the (1)(3)Sigma(-)(u) state. The ground state dissociation energy D-0 is predicted to be 23164 cm(-1).