This symposium was held in honour of Yuri Oganessian for his laurea honoris causa conferred by the University of Messina, and to celebrate Giorgio Giardina's 60th birthday.The aim of the symposium was to focus on the new projects and new lines of research in nuclear physics that will be developed in the main laboratories and research centres during the next 1020 years.The main emphasis was on the discussion (from both the experimental and theoretical viewpoints) of properties of nuclei under extreme conditions (at large mass numbers, at large isospin, at high temperature, and at nuclear...