This is a review of researches on the calculation of the electronic characteristics of a free or perturbed metal surface; these include the electron density, the potential, the spectrum of surface states, the work function, the surface energy, response of the surface to an electric field, the chemisorption of atoms, and the adhesion of two metals. Preference is given to papers that employ the theory of the ground state of an inhomogeneous electron gas, the ``density-functional method''. The various approximations to the density-functional used in the calculations, and the various models of the lattice (``jelly'', pseudopotential), are analyzed as to their applicability. Various sorts of experimental data are discussed on the basis of the theoretical results.