Graphene is a material with unique properties, which attract a lot of interest and offer technologically advanced features. In master’s thesis I present graphene and its properties, describe the crystal structure and show the theoretical calculation of the dispersion relation of energy bands in graphene, using the tight binding method. In the following chapter I present the experimental methods which I have exploited to perform the measurements – helium atom scattering (HAS), X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS) and angle resolved ultraviolet photoelectron spectroscopy (ARUPS). In the experimental part, I present the formation of graphene films on the surface Ni(111), which I have created by chemical vapor deposition of ethylene. By X-ray photoelectron spectroscopy measurements, I have determined the type of produced graphene film and distinguished different graphene phases (epitaxial and rotated) from the carbide phase. I have found that the temperature of the sample and the concentration of dissolved carbon in the substrate (this is associated with the pressure and the time of ethylene dosing) play crucial role on the type of the graphene phase formed on Ni(111). Using helium atom scattering I have measured surface roughness during ethylene dosing. Measurements have shown that the carbide phase is more ordered than graphene phases. By using ultraviolet photoelectron spectroscopy and angle-resolved ultraviolet photoelectron spectroscopy, I have determined the structure and dispersion of the valence band. In the case of the bi-layer graphene, I observed the shift of the π-states towards lower binding energies, showing that the rotated phase in bi-layer graphene couples with Ni(111) surface weaker than epitaxial graphene. I have made a comparison of the dispersion relation for the epitaxial graphene on the Ni(111) and the bi-layer graphene on the surface of nickel. Measurements are in good agreement with theoretical calculation of dispersion, showing energy gap for epitaxial graphene (2,4 eV) and gapless bi-layer graphene.