"Understanding star formation remains one of the greatest challenges of modern astronomy. Indeed in this field the progresses have been limited due, first, to the huge dynamics of spatial and temporal relevant scales and, second, the great variety and non-linearity of the physical processes involved in the formation of stars. The present proposal will contribute to provide a complete and coherent picture of the star formation process by self-consistently following the evolution of the interstellar matter from the very diffuse gas up to the protostars. This will be achieved by performing a series of heavy MHD numerical simulations with an adaptive mesh refinement code while subdivising the problem in three major steps namely the formation of large scale molecular clouds, the formation of star forming cores and the collapse of protostellar cores. In particular, the impact of the magnetic field and the radiative processes will be self-consistently treated using appropriate schemes. At each step, comparisons with both analytical models and observations will be performed by using existing models or developing new ones and calculating synthetic observations. The simulation results will also be used to test and improve the methods and the algorithms used by observers to extract the physical information from their data. An existing database, where the simulation results are available, will be further developed. The present proposal pursues two aims: i) achieving a global understanding of the star formation process, in particular by elucidating the link between the physical properties of the large scale ISM and the characteristics of the protostars, such as their mass, magnetisation and angular momentum ii) provide a better insight of the structure, nature and role of the magnetic field and the turbulence from the diffuse to the dense parts of the ISM."