"This is an interdisciplinary proposal that explores a rich new vein of interaction between algebra in the form of `noncommutative geometry' and deep applications in mathematical physics including elementary particle physics and quantum gravity. These are all areas of existing excellence in the EU and the innovative proposal will help to maintain the EU competiveness and high profile in these areas and to promote new synergies by their interaction. Specifically, it is proposed to develop a general theory of factorisation of noncommutative geometrical structures or conversely of building up such structures from the same data on each factor of an algebra factorisation, and to apply this new mechanism for construction of noncommutative geometries to quantum groups, quantum spacetimes (which includes astrophysical implications related to the ESA/NASA GLAST initiative) and other applications as indicated. The project will consolidate the novel pure mathematical work in the Researcher's recent PhD thesis and related papers and add to this new extensive training on the quantum groups and mathematical physics sides, thereby providing an enhanced platform for his long term career development. The training will also enhance collaboration with and transfer knowledge back to the researchers `home base' in Granada or to wherever the Researcher finally settles (which is expected to be in Spain in the long term). The training will also include organising workshops, speaking at high level national and international conferences and high-level scientific writing."