We present a theory of the dynamics of monatomic liquids built on two basic ideas: (1) the potential surface of the liquid contains three classes of intersecting nearly harmonic valleys, one of which (the `random' class) dominates the potential surface and consists of valleys which all have the same depth and normal-mode spectrum; and (2) the motion of particles in the liquid can be decomposed into oscillations in a single many-body valley, and nearly instantaneous inter-valley transitions called transits . We review the thermodynamic data which led to the theory, and we discuss the results of molecular dynamics (MD) simulations of sodium and Lennard-Jones argon which support the theory in more detail. Then we apply the theory to problems in equilibrium and nonequilibrium statistical mechanics, and we compare the results to experimental data and MD simulations. We also discuss our work in comparison with the quenched normal-mode and instantaneous normal-mode research programmes and suggest directions for future research.
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