The last decade has brought a number of new results related to the thermodynamic fundamentals of surface science. Increasing the generality and rigor of known methods and obtaining new relationships make necessary supplementing the previous review of the author [A.I. Rusanov, Surf. Sci. Rep. 23 (1996) 173-247] to provide a fresh insight into the modern higher-level state of surface thermodynamics. A deeper understanding of such basic notions of surface thermodynamics as dividing surface, excess surface stress (surface tension), transversal surface tension, line tension, and mechanical equilibrium is reviewed for curved interfaces. At the same time, the development of the local thermodynamics (including surface layers with a real surface stress) is exhibited with the gateway to mechanochemistry, which is practically a department of surface science for solids. The chemical approach to the thermodynamics of nanoparticles is described and illustrated by examples. Polymorphous transformations in nanoparticles are characterized. New relationships for thin wetting films (on the surface, in slits and pores) are given, and various cases of non-uniform (in thickness) films are analyzed. The modern theory of an equation of state of an adsorbed monolayer is formulated, and the survey of old and new equations of state is given within the hierarchy of approximations.