"This proposal is concerned with a joint Indo-European presearch programme on the field of moduli spaces. Moduli spaces are basic and central objects that emerge in the most natural classification problems in geometry. Their importance has been emphasized over the years due to the relation of these spaces with areas of mathematics so diverse as algebraic geometry, differential geometry, topology, arithmetic geometry, algebra, global analysis and, perhaps more surprisingly, with theoretical physics.The programme is centered around the following three areas of this field:(1) moduli spaces and geometric structures.(2) moduli spaces and physics.(3) moduli spaces and arithmetic geometry.There are four European partners involved: Consejo Superior de Investigaciones Científicas (Madrid, Spain), University of Oxford (Oxford, UK), Université Pierre et Marie Curie (Paris, France) and Aarhus Universitet (Aarhus, Denmark), and four Indian partners: Tata Institute for Fundamental Research (Mumbai, India), Chennai Mathematical Institute (Chennai, India), Institute of Mathematical Sciences (Chennai, India) and Indian Institute of Science (Bangalore, India).The partners have strong overlap of interests and complementary expertise. The main objective of this programme is to establish new collaborations and reinforce existing collaborations inside Europe and between Europe and India in the field of moduli spaces, as well as training young researches. This will be done through the exchange of both experienced and early stage researchers, and the organization of conferences, specialized workshops and schools."