The main aim of this proposal is to set up an International Research Network inn Theoretical Immunology that involves both experimental and theoretical immunologists. This Network will create new collaborations and reinforce existing ones in order to develop a lasting and fruitful research cooperation between all the partners. Other objectives of this proposal are (1) Establish a lasting and fruitful research cooperation between the experimental and theoretical immunologists of the network with the aim to provide immunology with a more quantitative basis. (2) Establish a lasting and fruitful research cooperation between the different groups that work in theoretical immunology, with the aim to discuss, compare, test and validate different modelling approaches. (3) Train the new generation of theoretical immunologists, with the aim to exchange postgraduate students and research fellows, so that they benefit from the broader knowledge, skills and tools provided by the Network. (4) A final objective of the Network is to develop, by means of the Staff Exchange Scheme, four long-term directions for modelling in immunology. In particular, (i) To develop stochastic models for the motion of pathogens and of cells of the immune system, validated by comparing with experiments. (ii) To build a model of the immune system as a whole using stochastic dynamics of interacting populations. We aim to understand how the system maintains its diversity of millions of lymphocyte populations and how populations of naive and memory cells are maintained. (iii) To develop stochastic models of T cell and B cell maturation. (iv)To develop models of autoimmunity.