Cohomology of infinite-dimensional Lie algebras and characteristic classes of foliations

A theory of characteristic classes of foliations is discussed which is based on the cohomology of infinite-dimensional Lie algebras. One of the original results of the article is a theorem stating that the characteristic classes are nontrivial.Translated from Sovremennye Problemy Matematiki, Itogi Nauki i Tekhniki, Vol. 10, pp. 179–285, 1978.