Chemical thermodynamics is of pivotal importance in chemistry, physics, the geosciences, the biosciences and chemical engineering. It is a highly formalised scientific discipline of enormous generality, providing a mathematical framework of equations (and a few inequalities) which yield exact relations between macroscopically observable thermodynamic equilibrium properties and restrict the course of any natural process. This review focuses on internal energy and enthalpy of nonelectrolyte liquids, vapours and gases, either pure or mixed (chemically non-reacting). After presenting the basic postulates, i.e., the first and the second law, the fundamental property relations in the internal energy representation and in the equivalent entropy representation are given. Alternative primary functions, such as enthalpy, Gibbs energy and Massieu function are introduced via Legendre transformations, together with the corresponding alternative forms of the fundamental property relations. Maxwell relations and practically important equations for constant-composition fluids are considered, the focus being on the temperature dependence and the pressure dependence of the internal energy and enthalpy, and relations involving heat capacities as well as the thermodynamic sound speed follow. The concepts of property changes of mixing and of excess properties for liquid multicomponent mixtures are introduced, and a few selected empirical correlations describing the composition dependence of excess molar properties, such as a generalised Kohler equation, are presented.