The main goal of the research project that I propose for the next three years is the study of the electronic properties of nanostructures at the atomic scale. The investigation will be performed by means of low temperature scanning tunnelling microscopy/spectroscopy in ultrahigh-vacuum environments (UHV-LTSTM), a unique technique which allows the study of these electronic properties in a local way with atomic resolution. Thanks to this technique it will be possible to get the local electronic information of the nanostructures with ultimate energy resolution (<1meV) and also to modify the systems in a controlled way by direct manipulation using the STM tip. This will open the possibility to selectively modify the local environment of the nanostructures to study and also to create new nanostructures using as elemental building-blocks atoms and/or individual molecules. The investigation will be structured in three main research lines: On one side the electronic properties of nanostructures electronically decoupled from the substrate by means of ultrathin insulating films will be studied Two main kind of nanostructures will be examined; bidimensional metallic films and molecules both in single and self-assembled arrangements. In a second line these same nanostructures, now adsorbed on epitaxial graphene, will be investigated. Special emphasis will be put in the influence of the Dirac quasiparticles of graphene in the electronic properties of the nanostructures and also in understanding and/or controlling how the adsorption of these nanostructures locally or even globally modify the electronic properties of graphene itself. The third research line will be focused on the study of phase transitions in the metal semiconductor systems Pb/Si(111), Pb/Ge(111) and Sn/Ge(111) at 4K. One of the fundamental questions to understand the temperature evolution of these 2D systems is precisely to know which is the true ground state at the lowest temperature.