"The Atacama Large Millimetre/submillimetre Array (ALMA) is the major global project for ground-based astrophysics currently under construction. Europe, through the European Organization for Astronomical Research in the Southern Hemisphere (ESO), is one of the three major partners of this project. ALMA will start Early Science operations in 2010 and Full Science operations in 2012. When completed, ALMA will allow astronomers worldwide to carry out transformational science and it will be the leading facility of its type in the foreseeable future. To exploit the full scientific potential of this revolutionary instrument, Europe has to train and develop a new generation of young researchers and strengthen the connections between the various institutes throughout Europe where there are already strong groups of millimetre/submillimetre astronomers. We believe that the best way of achieving this goal is to promote the scientific development and mobility of young researchers through a fellowship programme. ESO has been running a highly successful Fellowship Programme for the last three decades. In the framework of this programme fellows come to the ESO premises to carry out top class scientific projects of their choice and to learn and develop additional skills related to the various aspects of of the organization (from science operations to instrument development and public outreach). We propose to extend our existing Fellowship Programme in Garching and offer the possibility to Fellows to carry out the research programme of their choice either at the ESO headquarters or in any of the European institutes that are participating in the European ALMA Regional Center. The proposed extension of the ESO Fellowship Programme will enhance the transnational mobility and transfer of knowledge character of the Programme and will allow candidates to choose from a wider range of options for their science projects, career development and location of the Fellowship"