When a physical system involves many coupled degrees of freedom it is usually impossible to solve exactly the equations of motion describing the microscopic time evolution of the system (e.g. Newton's equations for more than two interacting particles). This is the notorious 'many-body
problem' which occupies the time of a multitude of physicists worldwide.

Fortunately, many quantities of interest do not require detailed knowledge of individual particle motion, but are average quantities (e.g. the pressure of a gas at a boundary arises from many
collisions with the gas molecules): A statistical description becomes appropriate - the 'statistical mechanics' of Boltzmann and Gibbs.

In this colloquium I will discuss the statistical mechanics of liquids and how this can be cast in the form of a variational theory - the density functional theory (for which Walter Kohn received the 1998
Nobel prize in chemistry). All quantities of interest can be calculated by minimizing a certain functional with respect to the particle density distribution. Particular attention will be given to the very simple
model system of hard spheres for which geometrical arguments can be employed to construct accurate approximate functionals.