The aim of the school is to promote mathematical research and facilitate contacts between Italian and foreign researchers in this field. Meetings dedicated to the exposition and examination of questions relating to various branches of mathematics and its applications will be organised for researchers and scholars. The main objective of the school is to promote contacts between specialists in the various mathematical fields and to foster contacts between these specialists and young researchers. The main focus will be on applications of mathematical analysis to the various fields of physics, mathematical economics, etc. In addition, the school proposes to collaborate with other similar existing courses, such as the International Summer Centre for Mathematics (CIME). This will be done through the organisation of joint courses and the organisation of courses that can serve as an introduction to higher studies.