During the last thirty years, the postgraduate course stricto sensu reached its maturity. Its main purpose is to prepare university professors, by updating them in specific areas of knowledge, and teaching them how to carry out scientific works. Few major advisors, little financial support and lack of association with other courses and institutions are the limiting factors. The limits related to the postgraduate students are the diversity, the deviation from the professional activity and the isolation of the students in a strange environment. The advantages brought by this course justify investments in its growth and consequent development of the university.