The book is devoted to methods of studying linear systems and problems, the description of which leads to equations with positive (in relation to some semi-order) operators .. The first chapter is devoted to basic concepts (semi-order, various classes of cones and their geometry, methods of perfectly convex sets and smooth points, etc.) ). Second - applications to spectral problems (mainline eigendirections, leading and peripheral eigenvalues, focusing and sharp operators, oscillation theorems, etc.) ). The third chapter studies various iterative procedures, methods for obtaining estimates of spectral radii, spectral gaps, posterior estimates in the problem of eigenvectors, and t. d. The last chapter shows the applications to the problems of forced oscillations in automatic control systems and their construction by the method of harmonious balance, problems of stability and absolute stability, etc. The main part of the book consists of results previously published only in journal articles .. A large number of exercises of different difficulty.