We report the near-edge x-ray absorption fine structure (NEXAFS) spectrum of a single layer of graphite (graphene) obtained by micromechanical cleavage of Highly Ordered Pyrolytic Graphite (HOPG) on a SiO2 substrate. We utilized a PhotoEmission Electron Microscope (PEEM) to separately study single- double- and few-layers graphene (FLG) samples. In single-layer graphene we observe a splitting of the pi* resonance and a clear signature of the predicted interlayer state. The NEXAFS data illustrate the rapid evolution of the electronic structure with the increased number of layers.