Magnetic surface levels represent a new fundamental quantum phenomenon. Its essence is that in the surface layer of a metal placed in a weak magnetic field a system of energy levels arises for electrons moving along shallow arcs whose ends rest upon the surface of the metal. This phenomenon is due to the specular reflection of electrons at the metal surface, which gives rise to a quantized periodic motion of electrons along these ‘skipping’ trajectories. The spectrum of the system of magnetic surface levels manifests itself as an oscillatory dependence of the surface-impedance on the weak magnetic field. The impedance oscillations are due to resonant absorption of microwave radiation in electron transitions between the levels.