This book is based on the lectures given at the “Euroschool on Exotic Beams” and collects contributions which address topics from the traditional core of the field of exotic nuclei like nuclear structure far from stability, discussing recent theoretical developments and state-of-the-art experimental methods. It provides also new perspectives in nuclear astrophysics and in applied areas such as gamma-ray emission imaging. The contributions are written with a pedagogical approach and carefully edited in order to provide the readership with a clear and fluent reading. The book is intended for PhD students and young researchers who are approaching the new research lines in nuclear physics with exotic nuclei. Only basics concepts on quantum mechanics and nuclear physics are requested to follow and master the covered arguments.