Graphene is a single sheet of graphite. While bulk graphite is semimetal, graphene is a zero bandgap semiconductor. Band structure calculations show graphene has a linear energy dispersion relation in the low energy region close to the Dirac points where the conduction band and the valence band touch. Carriers in graphene are described as massless Dirac fermions in contrast to massive carriers in normal metals and semiconductors that obey a parabolic energy dispersion relation. The uniqueness of graphene band structure indicates its peculiar electronic transport properties. In this thesis work, single- and multi-layer graphene films epitaxially grow on either the Si face or the C face of SiC substrates in a homemade induction vacuum chamber by thermal decomposition of SiC at high temperatures. The surface morphology and crystal structure of epitaxial graphene are studied with surface analysis tools. The transport properties of epitaxial graphene are studied by magnetotransport experiments. An epitaxial graphene film turns out to be a multilayered graphene because carriers in epitaxial graphene act as those in single layer graphene. Top gated and side gated epitaxial graphene field effect transistors (FETs) have also been successfully fabricated. These systematic studies unambiguously demonstrate the high quality of epitaxial graphene and the great potential of epitaxial graphene for electronic applications