The modern forms of key equation of surface thermodynamics are analysed. The generalized Laplace equation includes anisotropy of surface tension and the second order curvature terms. The generalized Young equation includes the line work and the line curvature. The generalized Gibbs adsorption equation for solid surfaces includes anisotropy of surface tension and of chemical potentials and is written also in terms of surface work. Universal interrelations between surface energy, cohesive energy, and the vaporization heat are derived, and their dependence on the surface structure of matter is established. The role of the surface and line tensions in formulation of the equilibrium and stability conditions is discussed.