Theoretical studies of graphene began long before the first real samples were obtained (Wallace, 1947). Calculations performed in the 1930s and 1940s showed that a free two-dimensional film must be thermodynamically unstable. For this reason monolayer structures were obtained only on the surface of bulk materials. The first steps to make single carbon layers were made in the 1960s and 1970s using the reduction of graphite oxide from colloidal solutions (Boehm et al., 1962a, b) and the method of chemical vapor deposition (CVD) of hydrocarbons on metal substrates (Eizenberg and Blakely, 1979) or on their carbides (Aizawa et al., 1990). It has been shown that a high-temperature treatment of silicon carbide with evaporation of silicon leads to the formation of carbon film, that is, the so-called epitaxial growth is realized (van Bommel et al., 1975; Forbeaux et al., 1998). However, in all the works listed above, carbon films with a thickness of at least 20–30 layers were obtained, which were not inherently graphene. A detailed review of early experiments on the preparation of thin graphite layers was given in Jang and Zhamu (2008).