Although the boron hydrides are well-known in the literature, the aluminum hydride chemistry is limited to very few systems such as AlH3, its dimer, and its polymeric form. In view of the recent experimental studies on the possible existence of the aluminum hydrides, herein, we have undertaken a systematic study on the electronic structure and properties of these aluminum hydrides. Under this, we have studied different classes of hydrides, viz., closo (AlnHn+2), nido (AlnHn+4), and arachno (AlnH(n+6)), similar to the boranes. All the aluminum hydrides are found to have exceptionally large highest-occupied molecular orbital-lowest-unoccupied molecular orbital gaps, low electron affinities, large ionization potentials and also large enthalpy and free energy of atomization. In addition, most of the structures are also found to have high symmetries. These exceptional properties can be indicative of the pronounced stability, and hence, it is expected that other aluminum hydride complexes can indeed be observed experimentally.