The European Exascale Software Initiative (EESI) goal is to build a European vision and roadmap to address the challenge of the new generation of massively parallel systems composed of millions of heterogeneous cores which will provide Petaflop performances in 2010 and Exaflop performances in 2020. These capabilities lead to outstanding technological breakthrough possibilities in computations and simulations which will be reached only if an international cooperation work program is set up.This will be done through a set of conferences and work groups involving a very large number of HPC European actors and users. They will investigate where Europe stands in the overall international HPC landscape and competition, what are its strengths and weaknesses, and whether such or such topics and challenges should be addressed inside or outside Europe. EESI will also identify the sources of competitiveness for Europe induced by the development of Peta/Exascale solutions and usages.The overall challenge must be faced at worldwide level to be attainable. A close collaboration with the EU PRACE project which is preparing the tier-0 level of the European HPC ecosystem, will be implemented. Coordination with the International Exascale Software Project (IESP) launched by The Department Of Energy (Office of Science), National Science Foundation and Department Of Defense is planned. The project leader of IESP, Jack Dongarra, and the Japanese executive member of IESP, Satoshi Matsuoka, are contributing participants of EESI.Expected outputs of the project are a roadmap and a set of recommendations shared by the European HPC community, on tools, methods and applications to be developed for this new generation of supercomputers. Coordination with international actors working on the same goal will have been effectively established.