Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the global equilibrium geometries and electronic structure of neutral, cationic, and anionic aluminum clusters containing up to 15 atoms. The total energies of these clusters are then used to study the evolution of their binding energy, relative stability, fragmentation channels, ionization potential, and vertical and adiabatic electron affinities as a function of size. The geometries are found to undergo a structural change from two dimensional to three dimensional when the cluster contains 6 atoms. An interior atom emerges only when clusters contain 11 or more atoms. The geometrical changes are accompanied by corresponding changes in the coordination number and the electronic structure. The latter is reflected in the relative concentration of the s and p electrons of the highest occupied molecular orbital. Aluminum behaves as a monovalent atom in clusters containing less than seven atoms and as a trivalent atom in clusters containing seven or more atoms. The binding energy evolves monotonically with size, but Al-7, Al-7(+), Al-7(-), Al-11(-), and Al-13(-) exhibit greater stability than their neighbors. Although the neutral clusters do not conform to the jellium model, the enhanced stability of these charged clusters is demonstrated to be due to the electronic shell closure. The fragmentation proceeds preferably by the ejection of a single atom irrespective of the charge state of the parent clusters. While odd-atom clusters carry a magnetic moment of 1 mu(B) as expected, clusters containing even number of atoms carry 2 mu(B) for n less than or equal to 10 and 0 mu(B) for n > 10. The calculated results agree very well with all available experimental data on magnetic properties, ionization potentials, electron affinities, and fragmentation channels. The existence of isomers of Al-13 cluster provides a unique perspective on the anomaly in the intensity distribution of the mass spectra. The unusual stability of Al-7 in neutral, cationic, and anionic form compared to its neighboring clusters is argued to be due to its likely existence in a mixed-valence state.