Employing multireference variational (MRCI) and coupled cluster (CC) methods combined with quadruple-zeta quality correlation-consistent basis set, we have Studied 36 states of the magnesium diboride (MgB2) molecule as well as 17 states of the experimentally unknown diatomic MgB. For all states of MgB2, we report geometries, atomization energies, and dipole moments, while for the first 5 states, potential energy profiles have been also constructed. The ground state is formally of (1)A(1) V-shaped symmetry with an atomization energy of 108.1(109) kcal/mol at the MRCI(MRCI + Davidson correction) level. The first excited state (B-3(1)) is less than 1 kcal/mol above the (X) over tilde (1)A(1) state, with the next state of linear Mg-B-B geometry ((b) over tilde Sigma(-)) located 10 kcal/mol higher. In all states, bent or linear, the bonding is complicated and unconventional because of the extraordinary bonding agility of the boron atom(s).