Graphene is the first known truly two-dimensional material. Since its discoveryrnin 2004, it has gained lots of attention due to its extraordinary electronic propertiesrnand mechanical strength, and it might supersede or complement silicon in thernfuture.rnWithin this thesis, graphene samples were first prepared using the original methodrnof micromechanical cleavage. A high-throughput optical technique was developedrncapable of obtaining the layer numbers from sheet contrasts in the luminancernchannel of reflected light micrographs. Using a microsoldering technique, electricalrncontacts drawn from liquid indium were deposited on the prepared sheets.rnFrequency modulated Kelvin probe force microscopy (FM-KPFM) was then usedrnto measure the surface potential of graphene mono- and multilayers while the carrierrndensity was tuned. It was found to agree with tight-binding calculations. Inrncontrast, the surface potential obtained from amplitude modulated KPFM (AMKPFM)rnshowed superimposed effects of the unscreened gate electrode.rnSimultaneously with measurements using FM-KPFM, the amplitude of the secondrnsideband was recorded. It exposed a minimum at the Dirac point within graphene.rnThis indicates strong sensitivity to the quantum capacitance, which is directlyrnrelated to the density of states at the Fermi level.rnThe results recommend FM-KPFM combined with detection of the second sidebandrnas a valuable tool to gain spatially resolved and quantitative information on intrinsicrnelectronic properties of two-dimensional materials. Measurements are performedrnin non-contact mode and involve no current flow that may disturb the electronicrnstructure. The technique may therefore be used to image inhomogeneitiesrnof the carrier density on a local scale, or to quantify the size of band gaps in thernincreasing class of two-dimensional semiconductors.