The generalized Liouville equation is studied in a new light using the Lie derivative of a differential form with respect to a vector field.

It is demonstrated with the help of an example that in general one cannot derive a constant of motion from a conservation law even if one assumes that the field under consideration and all its derivatives with respect to the space coordinates vanish rapidly as the space coordinates tend to infinity.

Various aspects of the integrability of dynamical systems are discussed with the help of the singular point analysis. In particular the connection with the Painlevé property is described. Several examples will serve as illustrations.

A simple model of an exciton-phonon system is studied in connection with quantum chaos.

The analysis of interacting relativistic many-particle systems provides a theoretical basis for further work in many diverse fields of physics. After a discussion of the nonrelativisticN-particle systems we describe two approaches for obtaining the canonical equations of the corresponding relativistic forms. A further aspect of our approach is the consideration of the constants of the motion.