Tests of the Standard Model (SM) of Particle Physics and the search for New Physics (NP) is a central issue in the European program in High-Energy Physics. Weak decays of heavy hadrons have a unique potential for the extraction of SM parameters, the study of CP violation, and the search for NP. Among these, decays of B mesons into three final hadrons are of huge phenomenological interest. They have been studied experimentally at B factories and at the LHC, and will be a cornerstone in the physics program at Belle-II. However, the theoretical basis for such processes has yet not been developed. Through this project, we will establish the theoretical grounds for the description of non-leptonic three-body B decays, from basic principles to phenomenological applications. The theoretical description of three-body decays requires a generalization of the theory of non-leptonic two-body B decays, which is by now well established. It involves factorization of perturbative and non-perturbative physics --most conveniently achieved in the framework of Soft-Collinear Effective Theory (SCET)--, the calculation of perturbative kernels, and the study of non-perturbative matrix elements. However, this generalization is non-trivial and requires addressing new issues and facing new challenges, making this a highly innovative project. We are three the participants in this action: - Javier Virto (Main Researcher), with a wide experience in the theory and phenomenology of B decays, will be the driving force in this project, while receiving an intensive training from two of the developers of the theory of hadronic B decays. - Iain Stewart (US partner), developer of Soft-Collinear Effective Theory. - Martin Beneke (EU Host), developer of the QCD Factorization approach and SCET in position space.