1. In the beginning we follow widely the introduction of the review article by M.E. Fisher, Rept. Prog. Phys. 30, 615 (1967). Compare also the review article by L.P. Kadanoff et al, Rev. Mod. Phys. 39, 395 (1967)
2. Depending on the number of experimentally available variables one may have a critical point, a critical line (λ-line) or even a critical surface, etc. There exist other special points, for example the common end point of a triple point line and three critical lines, called a tricritical point. These points can be described in the framework of this theory, too. They differ from normal critical points by the number of conditions necessary to reach such a point.
3. P. Weiss, J. Physique 6, 661 (1907); Arch. Sc. phys. et nat. 31, 401 (1911). The first theory which described a phase transition (for a liquid-vapor system) is due to J.D. van der Waals, Doctoral dissertation, Leiden (1873); Die Kontinuitdt des gasförmigen and flüssigen Zustands I and II. Verlag J.A. Barth (Leipzig, 1899 and 1900).
4. We hope that the reader does not get confused since as usual β is used for the critical exponent of the order parameter and the inverse temperature.
5. B. Widom, J. Chem. Phys. 43, 3898 (1965).