The book outlines a number of basic ideas and methods used to study ordinary differential equations. Elementary methods of integration are considered from the point of view of general-thematic concepts (resolution of features, Lie groups of symmetries, Newton diagrams, and t.). d. ). The theory of equations with first-order partial derivatives is presented on the basis of the geometry of the contact structure .. The book includes classical and modern results of the theory of dynamical systems. Structural stability , U-systems, analytical methods of local theory in the vicinity of a special point or periodic solution (normal forms of Poincaré) theory of phase portrait bifurcation when parameters are changed (soft and rigid excitation of autovibrations when stability is lost) , Feigenbaum period doubling, Dulac's Theorem et al. The book is designed for a wide range of mathematicians and physicists - from students to teachers and researchers.