The talk is devoted to the problem of finding polynomials thаt produce invariant algebraic manifold of a differential equation or a differential system. In detail we shall consider invariant algebraic manifolds of codimension n-1, where n is the order of the equation or the dimension of the related system. Our aim is to present a method of finding invariant algebraic manifolds in an explicit form. Further, we shall discuss a generalization of the method to other codimensions.
We shall pay some attention to applications of the theory of invariant algebraic manifolds including the problem of finding exact solutions and the integrability problem.