Graphene is a single layer of graphite sheet; one atom thick sp2-bonded carbon atoms organized on a plane. It has extremely interesting electrical properties, which offers various applications in a number of nanometer scale devices, potentially operating at high frequency ranges. Mechanically exfoliated single and multilayer graphene sheets are prepared on (100) oriented silicon wafers with 300 nm thermal oxide. These graphene layers are characterized by optical microscopy, Atomic Force Microscopy (AFM) and Raman Spectroscopy. A graphene feld effect transistor is fabricated on a 35x9 micron graphene sheet by manually applying the drain and source contacts using silver paint and using the silicon substrate as backgate. In this thesis, the production methods, characterization methods and electrical properties of graphene are investigated.