The present volume covers part of the material presented during the La Rábida 2009 International Scientific Meeting on Nuclear Physics, which can be considered heir of a well known series of triennial international summer schools on Nuclear Physics organized from 1982 till 2003 by the Basic Nuclear Physics group in the University of Sevilla. The 2009 meeting offered to graduate students and young researchers a broad view of the field of Nuclear Physics. In this volume, notes from four of the invited speakers can be found. The first two speakers covered theoretical topics: the role of electroweak interactions and of symmetry and supersymmetry in Nuclear Physics. The third set of notes is devoted to the description of the main experimental challenges faced today by Nuclear Physics, with special attention to the FAIR-GSI laboratory. Finally, the last set of lectures focuses on medical applications of Nuclear Physics, in particular on Ion Beam Therapy.