Description It details the results obtained by the author, connected with development of the following parts: Theory of Perron lower exponents, the freezing method, theory of exponential and sigma-exponents and their connection with characteristic, central, and general exponents, dependence of characteristic exponents of linear systems on exponentially decreasing perturbation and the theory of their stability with respect to small perturbations. The author considered the Lyapunov problem on the exponential stability of an ordinary differential system by linear approximation. The method of rotations by V. M. Millionschikov is systematically used. This volume is intended for postgraduates and students specialized in the field of differential equations