We have investigated the structure and properties of small metal clusters using all-electron ab initiotheoretical methods based on the Hartree-Fock approximation, density functional theory, and perturbation theory and compared the results of our calculations with the available experimental data and the results of other theoretical work. We have systematically calculated the optimized geometries of neutral and singly charged sodium clusters having up to 20 atoms, their multipole moments (dipole and quadrupole), static polarizabilities, binding energies per atom ionization potentials, and frequencies of normal vibration modes. Our calculations demonstrate the important role of many-electron correlations in the formation of the electronic and ionic structure of small metal clusters and form a good basis for further detailed study of their dynamic properties, as well as the structure and properties of other atomic cluster systems.