Theory of compositions

A survey of papers on the theory of compositions and their application to the investigation of manifolds in spaces with fundamental groups is presented.Translated from Itogi Nauki i Tekhniki. Problemy Geometrii, Vol. 10, pp. 117–145, 1978.I thank Érnst Gergardovich Neifel'd, whose paper 12] stimulated much of this survey, and who, moreover, showed me inestimable help in the formulation of my paper. In particular, he wrote Sec. 17.