The Institute of Mathematics of the Polish Academy of Sciences is a leading research institution in Poland in the area of pure and applied mathematics. A part of its mission is to provide high education for mathematicians, and to prepare them to work both in research and financial institutions, as well as in industry. Erasmus+ programme is supposed to contribute to some extent to implement this mission, and to positively influence the development of both students and employees, by stimulating their international mobility. The Project executed by the Institute of Mathematics of the Polish Academy of Sciences within the Erasmus+ programme assumed implementation of different kinds of actions aimed at increasing the mobility of students and employees according to the rules of the Erasmus Charter for Higher Education. The planned actions included two student mobilities for studies, two student mobilities for traineeships, one staff mobility for teaching, and one staff mobility for training. Apart from increasing the mobility, the project was aimed at the exchange of knowledge, ideas and experience, which is very important in the educational process. Eventually, there was one PhD student from our institute who participated in the project. The mobility he carried out was a traineeship in a Programme Country. He completed a two-month doctoral traineeship at Università degli Studi Mediterranea di Reggio Calabria, Italy, under the supervision of a world-class mathematician. The traineeship programme was tailored to the PhD studies programme, as well as to the individual research carried out by the student. The main result of the project was the scientific development of the student, the possibility to broaden his knowledge and to establish international cooperation, as well as the progress made with respect to doctoral thesis preparation. As for the long-term benefits, they undoubtedly include the cooperation that has been established between the two institutions, and the possibility to continue it in the future.