An electron in front of a metal surface experiences an attractive forc
e due to the induced image charge. Band gaps in the band structure can
prevent a penetration into the metal along certain directions. The Co
ulomb-like potential supports bound states in front of the surface whi
ch correspond to a hydrogen atom in one dimension. These image states
can be measured with high resolution by two-photon photoemission. The
adsorption of metals modifies the states. If the electrons can penetra
te into the metal, quantum-well states can develop corresponding to st
anding waves in the overlayer. Image states on small islands show the
quantization effects due to the lateral localization. The spectroscopy
of image states by two-photon photoemission permits the investigation
of growth and morphology of deposited metal layers, a well as the ill
ustration of fundamental quantum-mechanical effects.