Epitaxial films that are only several atoms layers thick exhibit interesting properties associated with quantum confinement. The electrons form standing waves, just like a violin string, clamped at both ends. In ultrathin lead films, this so-called `quantum size effect' (QSE) alters the physical properties of the film (such as the resistivity, work function, or thermodynamic stability) in such a way that the even and odd numbered layers show different behavior. Films consisting of 5 or 7 atomic layers are much more stable than films consisting of 4, 6, or 8 atomic layers, for example. The results of photoemission spectroscopy measurements give a detailed insight in the energy of the electrons in the film and explain the observed stability difference between the even and odd numbered layers. Another physical quantity that is expected to depend on film thickness is the distance between the first and second atomic layers. Low Energy Electron Diffraction experiments indeed provide the first quantitative experimental analysis of atom layer relaxations induced by the quantum size effect: even numbered layers show an increase of the distance between the first and second atomic layers with respect to the odd numbered ones. By making the link between atomic and electronic structure, the findings of this thesis have interesting and important implications for the science and technology of materials and devices of nanoscale dimensions.