  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)
vastly outnumbers the others and all whose members 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 QNM and INM research programs and suggest directions for
future research.
