For the diatomic aluminum nitride (A1N), we have constructed potential energy curves for 45 states employing multi-reference variational methods and quantitative basis sets. Thirty-six states are relatively strongly bound, five present local minima, and four are of repulsive nature. Almost all states are of intense multi-reference character rendering their calculation and interpretation quite problematic. Our tentative assignment of the ground state is (3)Pi, while a (3)Sigma(-) state is above by less than I kcal/mol. Our best estimate for the binding energy of the X-3 Pi state is D-0 = 56.0 +/- 0.5 kcal/mol at r(e), = 1.783 angstrom, in good agreement with the experimental values of D = 66 +/- 9 kcal/mol and r(e) = 1.7864 angstrom. The binding energy of the A(3)Sigma(-) state is very similar to the X state because they both correlate to the ground-state atoms, but the bond distance of the former is 0.13 angstrom longer. The first seven states can be tagged as follows: X-3 Pi, A(3)Sigma(-), a(1)Sigma(+), b(1)Pi, c(1 Delta), B-3 Sigma(+), and d(1)Sigma(+), a rather definitive order with the exception of X and A states.