The cell parameters, bulk moduli and electronic densities-of-states (DOS) of pure and vacancy defect AlN were computed using generalized-gradient approximation (GGA) and hybrid functional (B3LYP) computational methods within both plane wave-pseudopotential and localized Gaussian basis set approaches. All of the methods studied yielded cell parameters and bulk moduli in reasonable agreement with experiment. The B3LYP functional was also found to predict an optical band gap in excellent agreement with experiment. These methods were subsequently applied to the calculation of the geometry, defect state positions and formation energies of the cation (V(Al)) and anion (V(N)) single vacancy defects. For the V(Al) defect, the plane wave-pseudopotential predicted a significant retraction of the neighboring N away from the vacancy, while for the V(N) defect, only slight relaxations of the surrounding Al atoms towards the vacancy were predicted. For the computed DOS of both vacancy defects, the GGA methods yielded similar features and defect level positions relative to the valence band maximum, while the B3LYP method predicted higher separations between the defect levels and the valence and conduction bands, leading to higher energy occupied defect levels.