FMBS are expected to be quite different from those of bulk matter, being strongly conditioned by quantal size effects and by the dynamical properties of the surface of these systems. The study of the elec­ tronic and of the collective behaviour (plasmons and phonons) of FMBS and of their interweaving, making use of well established first principle quantum (field theoretical) techniques, is the main subject of the present monograph. The interest for the study of FMBS was clearly stated by Feynman in his address to the American Physical Society with the title "There is plenty of room at the bottom". On this occasion he said among other things: "When we get to the very, very small world - say circuits of seven atoms - we have a lot of new things that would happen that represent completely new opportunities for design" [1].