Nonlinear dynamics is developed in three different directions. Geometric qualitative theory of phase portraits, analysis (normal form, averaging, perturbative approach, asymptotics) and numerical simulations. This course is of basic level for undergraduate students who followed fundamental courses of linear algebra, differential calculus, topology and provides them an introduction to nonlinear dynamics. Nonlinear dynamics applications are ubiquitous in many sciences including physics, mechanics, biology and economics. In return, this field has received important feedback from modeling. We also include in this course presentations of such models.