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Time-dependent density-functional theory (TDDFT) is an approach to the
dynamical many-body problem which has become widely used in many areas
of physics, chemistry and materials science. This talk gives an overview
of the basic formalism of TDDFT and presents applications to atoms and
molecules in strong laser fields. We will discuss some of the problems
and critical issues of TDDFT for ultrafast, strong-field processes, and
present some recent developments in the construction of dynamical
exchange-correlation potentials beyond the adiabatic approximation.
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