The Ph.D. programme of the Mathematics Department prepares its students for either a professional or an academic career in the area of Mathematics and its applications. To this aim the Ph.D. program provides : - a training which is both of high quality and and wide spectrum; - opportunities for developing research skills; - actual research work in fields that are at the forefront of Mathematics and its many applications in different fields. The quality of our Ph.D program is ensured by the very high standards of research activity carried out in the Department (one of the best in Italy, according to the VQR) and the network of scientific contacts developed by the members of the Department of Mathematics. Moreover, belonging to the Vito Volterra graduate school gives further opportunities for scientific and cultural contacts. The graduate program in Mathematics offers training in Mathematics pure and applied. Studies in Pure Mathematics are aimed to those students that wants to work in one of the many fields of Pure Mathematics, a field which is widely represented in our Department, in all its facets, from the most abstract to the ones directly inspired by natural sciences. Studies in Applied Mathematics are instead aimed to those students that a particular interest for those problems in the natural sciences, economics and the social sciences that can be tackled with Mathematical tools; this program is also a way for widening scientific knowledge at large and giving a contribution to the development of Mathematics within other sciences. Study and research activities are structured as a three-year programme. Within the programme, students follow courses (in their first and second years), develop their own research with the direct guidance of a supervisor, and participate in other general research activities of the Mathematics Department. Information about these activities may be obtained by accessing the Department's homepage Beside specific, advanced courses of the Ph.D. programme, the Department offers specialized graduate courses. Provisional advisors are assigned to entering students, and at the end of the first year supervisors are chosen based on the research preferences of the students. In the first year, students focus on intensive course work, meant to provide tools for successful research. In the second year, in addition to some coursework, students develop their research project and regularly attend seminars and colloquia. Their activity is closely supervised and monitored; in particular, a comprehensive qualifying exam must be taken at the end of the first year. In the third year, after completing their research work, students present at a specific Department Forum the results of their Ph.D. thesis. Of course this is formally defended a few months later. Further information are available on www.mat.uniroma1.it/ricerca/dottorato