The elegance and general applicability of classical thermodynamics made a great impression on Albert Einstein as quoted: A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content, which I am convinced will never be overthrown, within the framework of applicability of its basic concepts. In this review, basic relationships between partial derivatives of internal energy, enthalpy, Helmholtz and Gibbs (free) energies are presented in a condensed and self-consistent “Thermodynamic Wheel of Connections” (TWC). As a support for experimentalists a complete set of first- and second-order partial derivatives of basic state functions (U, F, H, G) derived with respect to state variables (P, T, V, S) under isothermal, isobaric, isochoric and isentropic conditions are presented as a Table. The basic TWC-network remains unchanged when expanded by additional conjugative state parameter pairs, such as chemical potential – amount of substance and surface/interfacial tension – contact area. The extension enables characterization of first- and second-order phase transitions of bulk phases and interphases in terms of first-, second- and third-order partial derivatives of Gibbs energy as well as by first- and second-order partial derivatives of chemical potential and Derjaguin's disjoining pressure. Semi-three-dimensional interface (Guggenheim convention) state functions are derived by subtracting corresponding parameters from total state functions. Then properties become dependent on the location and extension of the interface. For truly two-dimensional mono-molecular Langmuir films (Gibbs convention), first- and second-order partial derivatives of basic interfacial state functions (Us, Fs, Hs, Gs) may be derived with respect to state variables (π, T, A, Ss) under isothermal, isobaric, isoareal and isentropic conditions. They are assembled as interfacial “Thermodynamic Family Three” (TFT) s. Replacing π by P, A by V and omitting upper index s it is converted to previously published TFT for bulk phases.