Single particle versus collectivity, shapes of exotic nuclei

29 pags., 21 figs.In this article some selected topics of nuclear structure research will be discussed as illustration of the progress reached in this field during the last thirty years. These examples evidence the improvement of our understanding of the atomic nucleus reached on the basis of countless experiments, performed to study both exotic nuclei (nuclei far-off the valley of stability) as well as nuclei under exotic conditions (high excitation energy/temperature or large angular momentum/rotational frequency), using stable and radioactive ion beams. The experimental progress, in parallel to the advancement of modern theoretical descriptions, led us to a much richer view of this fundamental many-body system. © Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016This work was supported by the Spanish Ministerio de Economía y Competitividad under contract FPA2014-57196-C5-4-P.Peer Reviewe