Recent years have seen an increasingly prosperous interaction between the fields of mathematics and theoretical physics. The development within the two fields has led to a stage where mathematicians and physicists are addressing and solving significant problems of common interest. Modern mathematical physics represents the common ground between these two activities, both in research and in teaching. Research in this field does not simply consist of explaining previously discovered physical concepts in rigorous terms (which in itself can be quite complicated). This research actively contributes to the development of current theoretical physics. It does so by attempting to determine to what extent the difficulties encountered are due to mathematical shortcomings or are related to the physical concepts introduced. Investigations along these lines have been conducted, with considerable success in recent years, both in relativistic field theory and statistical mechanics. As mathematical physics is a highly interdisciplinary subject, a frequent exchange of ideas between researchers in the field is necessary for its development. The aim of the International School of Mathematical Physics is to contribute positively to this exchange by establishing courses on topics of current interest. These courses will consist of a series of lectures for students given by Italian and foreign experts in the field. At the same time, personal contacts will be established, and fruitful but informal discussions will take place between the various participants. In Italian universities, with few exceptions, there continues to be a separation between physicists and mathematicians. Moreover, there are hardly any centres of mathematical physics that deal with modern theoretical physics problems. The creation of the International School of Mathematical Physics should contribute greatly to eliminating the current shortcomings and improving the overall situation.