Classical DFT allows the calculation of the equilibrium particle density and prediction of thermodynamic properties and behavior of a many-body system on the basis of model interactions between particles. The spatially dependent density determines the local structure and composition of the material. It is determined as a function that optimizes the thermodynamic potential of the grand canonical ensemble. The grand potential is evaluated as the sum of the ideal-gas term with the contribution from external fields and an excess thermodynamic free energy arising from interparticle interactions. In the simplest approach the excess free-energy term is expanded on a system of uniform density using a functional Taylor expansion. The excess free energy is then a sum of the contributions from s -body interactions with density-dependent effective potentials representing the interactions between s particles. In most calculations the terms in the interactions of three or more particles are neglected (second-order DFT). When the structure of the system to be studied is not well approximated by a low-order perturbation expansion with a uniform phase as the zero-order term, non-perturbative free-energy functionals have also been developed. The minimization of the grand potential functional in arbitrary local density functions for fixed chemical potential, volume and temperature provides self-consistent thermodynamic equilibrium conditions, in particular, for the local chemical potential. The functional is not in general a convex functional of the density; solutions may not be local minima. Limiting to low-order corrections in the local density is a well-known problem, although the results agree (reasonably) well on comparison to experiment.