The optimized structure and electronic properties of neutral and singly charged magnesium clusters havebeen investigated using ab initio theoretical methods based on density-functional theory and systematic post Hartree-Fock many-body perturbation theory accounting for all electrons in the system. We have systematically calculated the optimized geometries of neutral and singly charged magnesium clusters consisting of up to 21 atoms electronic shell closures, binding energies per atom, ionization potentials, and the gap between the highest occupied and the lowest unoccupied molecular orbitals. We have investigated the appearance of the elements of the hcp structure and metallic evolution of the magnesium clusters, as well as the stability of linear chains and rings of magnesium atoms. The results obtained are compared with the available experimental data and the results of other theoretical works.