Inertial manifolds are a modern tool in the qualitative theory of partial
differential equations, they contain the global attractor and allow for a
reduction to a finite-dimensional system. In this talk we give an
introduction and present a geometric approach to inertial manifolds for
nonautonomous dynamical systems. We present a new application to
time-dependent evolution equations. It is based on the attached paper which 
will appear in the Journal of Dynamics and Differential Equations.