-The development of new advanced techniques of synthesis and assembly, makes it possible to obtain low-dimensionality ' (e.g. thin films, nano-wires, nanoclusters or nanoparticles) or "supramolecular systems" whose physical and chemical properties are different both from those of molecules and from those of solid-state materials and make them extremely useful for applications in the field of new technologies. The physical and chemical properties of certain classes of nanomaterials will be considered, highlighting in particular their variation as a function of dimensionality and the size of the material. Particular attention will have the theoretical analysis of the main characteristics of nano systems and their relationship to the property of extended systems and of molecular systems.