  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 grid-based version of MIM is developed. Generalizations to open systems are
suggested. The set of methods covered makes it possible to effectively reduce
description in chemical kinetics.
  The most essential new element of this paper is the systematic consideration
of a discrete analogue of the slow (stable) positively invariant manifolds for
dissipative systems, {\it invariant grids}. We describe the Newton method and
the relaxation method for the invariant grids construction. The problem of the
grid correction is fully decomposed into the problems of the grid's nodes
correction. The edges between the nodes appears only in the calculation of the
tangent spaces. This fact determines high computational efficiency of the
invariant grids method.
