This PhD programme - unique in Italy - is devoted to the physics of particle accelerators and is promoted by the Istituto Nazionale di Fisica Nucleare (INFN). The goal of the PhD programme is to prepare young researchers thanks to the presence of facilities both in the University and in the INFN. Students are enrolled at Sapienza University of Roma but they can join research groups also based in other Universities and INFN laboratories in Italy. The lectures are devoted to improve the knowledge in Physics, acquired during the bachelor and master 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 at the INFN laboratories. All the theoretical courses can also be attended remotely via e-learning The intrinsically international nature of the community behind Accelerator Physics implies that most of the students can spend a significant amount of time abroad, in very high profile research infrastructures, like for instance, CERN.