Liquids lack the long-range order typical for solids. Collisional processes and short-range correlations distinguish liquids from dilute gases. Therefore, no idealized models comparable with the perfect gas or the harmonic solid are available for even simple liquids. During the last half of the 20th century a rapid progress has been made in our understanding of the microscopic structure and the dynamics of simple liquids. With advances in experiments (light and neutron scattering), theoretical analysis (statistical mechanics, kinetic theory of strongly correlated systems) and numerical tools (Molecular Dynamics and Monte Carlo simulations) a rather clear and complete picture emerged on the properties of simple atomic liquids. Since the last few decades a variety of more complicated systems are being studied: ionic, molecular and polar liquids, liquid metals, liquid-vapor interfaces, liquid crystals, and colloidal suspensions. In this lecture we will address the basic theory of the liquid state based on a statistical mechanical description of liquids. Topics that will be discussed include static properties of liquids, distribution function theories, perturbation theory and inhomogeneous fluids. We will conclude with an outlook to more complex fluids.

Introduction (week 1-2)

Liquid state, intermolecular forces

Liouville equation, BBGKY hierarchy

Statistical mechanics and ensemble averages

Static properties of liquids (week 3-4)

Particle densities and distribution functions

Computer simulations (MD and MC)

Diagrammatic expansions, virial expansion of the equation of state

Equation of state of a hard sphere fluid

Distribution function theories (week 5-6)

Static structure factor

Ornstein-Zernike direct correlation function

Percus-Yevick solution for hard spheres, mean spherical approximation

Outlook (week 7)

Perturbation theories

Complex liquids