This paper, like the note on integral geometry in the last number of the “Uspekhi” , is an addendum to my paper [1]. The main idea of the paper is contained in § 2, where we pose the problem of describing linear elliptic equations and their boundary problems in topological terms. The most important of the properties in the large of the solutions of these equations and problems are preserved under small deformations of the problem and must therefore be, in some sense, homotopy invariants. The discovery and study of these invariants is the right way to sort out the whole multiplicity of boundary problems for elliptic equations and to classify these problems. § 1 is introductory, and the reader may skim through it lightly if he wishes. In this section we introduce the basic definitions and notations and, in preparation for the discussion of general boundary problems for elliptic equations in § 2, we advance some general considerations about the nature of these problems. In the preparation of this paper M. S. Agranovich and Z. Ya. Shapiro have given me considerable help, and I take this opportunity of expressing my thanks to them.