IMT Institute for Advanced Studies Lucca is a public graduate school and research institute that focuses on the analysis of economic, societal, technological and cultural systems. Its interdisciplinary doctoral program includes courses held in English on campus in Lucca and one or more - not compulsory but strongly suggested - visiting period(s) abroad in research centres, universities, and companies. This is the framework for the realization of the Erasmus+ project, whose objectives are to promote mobilities of doctoral students and staff towards European destinations. The total number of mobilities under this project is 5 (other 20 student mobilities for traineeships were funded by the Erasmus+ Consortium led by the Scuola Superiore Sant'Anna Pisa): 3 student mobilities for traineeships and 2 staff mobilities for training. It is worth mentioning that this was the very first time that IMT staff had the opportunity of an Erasmus mobility for training and this sets an important milestone for the Institute. The preferred destinations of the Erasmus+ participants were academic: only one participant chose a research centre, namely the Jožef Stefan Institute, which is the largest Slovenian scientific research institute, whereas another student mobility for traineeship was carried out in the UK at the University of Cambridge (Department of Land Economy, Cambridge Centre for Climate Change Mitigation Research centre), and the last one in Germany at the University of Saarland (Department of Computer Science, Research Group in Modeling and SImulation). Both the staff mobilities for training were carried out in two different Swedish Institutions: the Chalmers University of Technology in Gothenburg and the Royal Institute of Technology (KTH) in Stockholm. Attained results and impact were extremely beneficial in a short time perspective (paper publication, closer collaboration with the host responsible person) and are also expected to positively affect the participants' careers in the long-run. In particular, one of the participants, not only obtained his doctoral degree shortly after the conclusion of the Erasmus mobility, but he decided to accept a position abroad in Europe (IBM Dublin).