  In this paper, we review the construction of low-dimensional manifolds of
reduced description for equations of chemical kinetics from the standpoint of
the method of invariant manifold (MIM). MIM is based on a formulation of the
condition of invariance as an equation, and its solution by Newton iterations.
A review of existing alternative methods is extended by a thermodynamically
consistent version of the method of intrinsic low-dimensional manifolds. A
grid-based version of MIM is developed, and model extensions of low-dimensional
dynamics are described. Generalizations to open systems are suggested. The set
of methods covered makes it possible to effectively reduce description in
chemical kinetics.
