Electronic states of a thin layer of material on a surface possess unique physical and chemical properties. Some of these properties arise from the reduced dimensionality of the thin layer with respect to the bulk or the properties of the electric field where two materials of differing dielectric constants meet at an interface. Other properties are related to the nature of the surface chemical bond. Here, the properties of excess electrons in thin layers of Xenon, Krypton, and alkali metals are investigated, and the bound state energies and effective masses of the excess electrons are determined using two-photon photoemission. For Xenon, the dependence of bound state energy, effective mass, and lifetime on layer thickness from one to nine layers is examined. Not all quantities were measured at each coverage. The two photon photoemission spectra of thin layers of Xenon on a Ag(111) substrate exhibit a number of sharp, well-defined peaks. The binding energy of the excess electronic states of Xenon layers exhibited a pronounced dependence on coverage. A discrete energy shift was observed for each additional atomic layer. At low coverage, a series of states resembling a Rydberg series is observed. This series is similar to the image state series observed on clean metal surfaces. Deviations from image state energies can be described in terms of the dielectric constant of the overlayer material and its effect on the image potential. For thicker layers of Xe (beyond the first few atomic layers), the coverage dependence of the features begins to resemble that of quantum well states. Quantum well states are related to bulk band states. However, the finite thickness of the layer restricts the perpendicular wavevector to a discrete set of values. Therefore, the spectrum of quantum well states contains a series of peaks which correspond to the various allowed values of the perpendicular wavevector. Analysis of the quantum well spectrum yields electronic band structure information. In this case, the quantum well states examined are derived from the Xenon conduction band. Measurements of the energies as a function of coverage yield the dispersion along the axis perpendicular to the surface while angle-resolved two-photon photoemission measurements yield information about dispersion along the surface parallel. The relative importance of the image potential and the overlayer band structure also depends on the quantum number and energy of the state. Some members of the image series may have an energy which is in an energy gap of the layer material, therefore such states may tend to remain physically outside the layer and retain much of their image character even at higher coverages. This is the case for the n = 1 image state of the Xe/Ag(111) system. The energies of image states which are excluded from the layer have a complex dependence on the thickness of the layer and its dielectric constant. The population decay kinetics of excited electronic states of the layer were also determined. Lifetimes are reported for the first three excited states for 1-6 atomic layers of Xe on Ag(111). As the image states evolve into quantum well states with increasing coverage, the lifetimes undergo an oscillation which marks a change in the spatial extent of the state. For example, the n = 2 quantum well state decreases substantially at 3-5 layers as the electron probability density in the layer increases. The lifetime data are modeled by extending the two-band nearly-free-electron approximation to account for the insulating Xe layer.