The research project TRANSITION aims at developing statistical mechanics tools, mainly based on large deviation theory, in order to compute rare events which are essential in the understanding of complex dynamical systems. The problems studied span a complete range between theoretical and applied mathematics issues in developing large deviation theory for complex dynamical systems, their numerical computations, and their application to real systems. The project applications focus mainly on turbulent flows relevant for climate dynamics, but applications to other turbulent flows and the solar system dynamics are also considered.