The book presents 12 lectures on the theoretical foundations of nonlinear dynamics of systems with a finite number of degrees of freedom (in the third edition of lectures, compared to the first, 3 lectures were added). A number of key issues are selected for discussion in the book, which relate to the fundamentals of nonlinear dynamics , Therefore, it is primarily aimed at students of natural specialties of universities , the Foundations of the Theory of Oscillations , Theory of Dynamical Systems , Sustainability and bifurcation theory , Fundamentals of Computer Science and Mathematical Modeling . The listed disciplines are included as sections in a more general theory of self-organization or synergetics. This book as a textbook on nonlinear dynamics will help students to more consciously choose their specialization in this area, and will also be useful to a fairly wide range of students and graduate students seeking to find their way into great science. The original publication is posted on the Scientific and Educational Portal on Nonlinear Dynamics, created by the Department of Radiophysics and Nonlinear Dynamics of Saratov State University