The main objectives of this course are to promote the acquisition of theoretical skills, both basic and advanced, for the study of nonlinear dynamical systems for which the time evolution of the corresponding states is determined, exclusively, by deterministic laws. These dynamical systems (also simple) can develop very complex behaviors, such as deterministic chaos. Therefore, an important purpose of the course is to train students so that they are able to use the main formal approaches for the study and the dynamical characterization of nonlinear systems. Finally, to concretize the application of the main analytical approaches and methods of the course to concrete examples, particular attention will be paid to carrying out exercises (in the classroom and at home).