Phase portraits, Phase diagrams, Fixed points and linearization, Stability theories, Autonomous and non autonomous systems, method of multiple scales, primary and secondary resonances, parametric and auto-parametric resonances, self excited systems, Floquet theory, bifurcations, shooting technique, Poincare section, introduction to quasi-periodic solutions, Chaos,  classifications, identification methods, routes to chaos, the escape from a potential well phenomenon, tangling.