This PhD programme, unique in Italy and therefore of national coverage, is oriented to the Accelerator Theory and Practice. It aims to prepare young researchers, profiting of the high level facilities both in the University and in the INFN, the National Institute for High Energy Physics. The lectures are devoted to improve the knowledge in Physics, acquired during the graduation courses, to the principles of the Accelerator Theory and to their applications in the different domains of this science. The students are offered both theoretical and practical lectures in the INFN laboratories. All the theoretical course can be attended, via e- learning, also from remote, to guarantee the national domain of the course. The intrinsically international nature of the community behind Accelerator Physics implies that most of the students spend a significant amount of time abroad, in very high profile research infrastructures, like for instance, CERN.