This volume contains the lectures presented by invited speakers at the IV La Rlibida International Summer School on Nuclear Physics. This was the IV edition of a summer school organized by our group every three years on topics related to nuclear physics. This Summer School was aimed mainly at young nuclear physicists, both theoreticians and experimentalists, engaged in research work at predoctoral or recent postdoctoral level. The topics treated in the three previous editions of the School were: "Heavy Ion Collisions", "Theory of Nuclear Structure and Reactions" and "Nuclear As trophysics". This year's School was entitled "Nuclear Physics at the Borderlines". Special emphasis was placed on those topics along which nuclear physics is ex pected to develop in the next few years. The aim of the School was to provide the attendants with an opportunity to get into close contact with experienced researchers and listen to their account of the present state-of-the-art in nuclear physics and the main future lines of development.