Binary and multiple stellar systems are numerous in our solar neighbourhood with 80 per cent of the solar-type stars being members of systems with high order multiplicity. The Contact Binaries Towards Merging (CoBiToM) Project is a programme that focuses on contact binaries and multiple stellar systems, as a key for understanding stellar nature. The goal is to investigate stellar coalescence and merging processes, as the final state of stellar evolution of low-mass contact binary systems. Obtaining observational data of approximately 100 eclipsing binaries and multiple systems and more than 400 archival systems, the programme aspires to give insights for their physical and orbital parameters and their temporal variations, e.g. the orbital period modulation, spot activity etc. Gravitational phenomena in multiple-star environments will be linked with stellar evolution. A comprehensive analysis will be conducted, in order to investigate the possibility of contact binaries to host planets, as well as the link between inflated hot Jupiters and stellar mergers. The innovation of CoBiToM Project is based on a multimethod approach and a detailed investigation, that will shed light for the first time on the origin of stellar mergers and rapidly rotating stars. In this work, we describe the scientific rationale, the observing facilities to be used and the methods that will be followed to achieve the goals of CoBiToM Project and we present the first results as an example of the current research on evolution of contact binary systems.