The singlet, triplet, and quintet states of AlB below about 30 000 cm(-1) are studied theoretically to facilitate spectroscopic investigations and for comparison with analogous calculations on the Al-2 and B-2 molecules. The ground state of AlB is X (3) Sigma(-) with a dissociation energy of 1.96+/-0.06 eV. The A (3) Pi state is computed to lie only 610 cm(-1) above the ground state. Since transitions from the (2)(3) Sigma(-) state to both the X (3) Sigma(-) and A (3) Pi states are predicted to be relatively strong, these transitions in the region of 17 000- 18 000 cm(-1) should be an excellent means of characterizing AlB and of determining the X-A separation. The adiabatic ionization potential to form the X (2) Sigma(+) ground state of AlB+ is estimated to be 7.05 eV. Overall the spectroscopy of AlB is much more similar to Al-2 than B-2.