Published in a limited academic edition of 390 copies. The book deals with the current situation in qualitative dynamics of the multiple arbitrarily nonlinear, generally considered physical lumped systems, and presents selection of research results employing the Poincare-Liapunov "direct" method of stability and applied topological dynamics. Themes are discussed in terms of the modern system theory approach, which is physical in nature although mathematical in form. Mathematical language is made as simple as possible. the results given are applicable to mechanical, electrical, electronic, automatic control and regulation systems, as well as in certain special problems of space dynamics. An up-to-date bibliography is included. The level is appropriate to graduate study lectures or pre-doctoral studies.