The course starts with the study of the exponential law of radioactive decay and its implications such as decay chains, equilibrium, natural radioactive series, etc. Then, all possible decay modes of atomic nuclei, not only those already well acquainted like alpha or beta emission, but also the recently discovered new forms of radioactivity like cluster or proton emission are described. For each decay mode the main characteristics in terms of involved nuclei, energies, selection rules etc. are explained and the most widely used theories are illustrated. For the recently discovered forms of radioactivity the experimental status of the art is also shown. Collective and independent particle nuclear models are treated in view of implications on radioactive decays. Finally, artificial and environmental sources of radioactivity are described and some applications of radioactivity such as the archaeological and geological dating are given. Some particular topics may be described with invited talks given by experts of the field.