The structures and stabilities of (Al2O3), (n = 1-10 and 30) clusters were studied by means of first principles calculations. The calculated results reveal that the global minima of small (Al2O3), (n = 1-5) clusters are cage structures with high symmetries, in which Al and O atoms are three- and two-coordinated, respectively, and are linked to neighbors via single bonds. Beyond (Al2O3)(5), we calculated both cage and cage-dimer structures for (Al2O3)(n) (n = 6-10), and the results show that, at this size range, cage-dimer structures are more stable than cage structures. Furthermore, an onion-like motif for (Al2O3)(10) was studied, and it is interesting to find that, at this size, the onion structure is more favorable than cage and cage-dimer structures. For large clusters, a shell structure of Al60O90 is suggested. Electronic properties and calculations on hydrogen adsorption of these aluminum oxide structures are reported, and we discuss their possible use as hydrogen storage materials.