The UNIFY exchange programme has two main scientific objectives. One objective is to gain new insights on the quantum mechanical description of the gravitational interaction, an outstanding fundamental problem in theoretical physics, of crucial importance to our understanding of the Universe and of the forces between its basic constituents. The other main objective is to explore recent developments in String Theory and Quantum Gravity in the fields of Cosmology, Black Hole Physics and Gauge Theory. The forthcoming years will bring unprecedented experimental discoveries in these fields of research and are sure to call for new explanations and to shape our attempts to construct an unifying theory of all interactions. These huge costly experiments (LHC, gravitational wave detection, PLANCK) are driven by theory, and theory is essential to analyse and interpret the vast data sets they produce. By creating an effective training platform, well connected to these efforts, UNIFY will play a major role in advancing EU research agendas in 'big science' projects that may lead to unprecedented insights into the fundamental workings of nature.UNIFY will achieve its goals by setting a challenging exchange programme that involves world leading CNRS laboratories in Paris, Humboldt Univ. and the Albert Einstein Institute in Berlin, and the Univ. of Santigago de Compostela and of Porto. The international partners that joined this collaboration are the Perimeter Institute for Theoretical Physics in Canada, the Yang Institute for Theoretical Physics and Caltech in the USA, and the Institute for the Physics and Mathematics of the Universe in Japan. UNIFY institutions will organize a number of thematic work programmes to push our present knowledge of the law's of nature to its very limit.UNIFY also includes in its exchange programme a strong dimension on the training of the next generation of theoretical physicists, as to establish long lasting collaborations between its partners.