The main purpose of the manual is to give as complete an idea as possible about the subject and methods of the general theory of dynamical systems. The manual provides elementary information from the general theory of dynamical systems, considers some issues of nonlinear dynamics, the theory of local bifurcations. Particular attention is paid to the issues of mathematical modeling of various dynamic processes. The presentation is accompanied by explanatory examples and recommendations, the chapters are provided with tasks and exercises. The manual is intended for students studying in mathematical, physical and mathematical and technical specialties.