This thesis is assessing the potential of the European rail passenger market with a 4 step model, with a gravity based trip distribution and assessment of level of service characteristics to determine total potential in demand and supply commissioned by Train2EU and Royal HaskoningDHV. The scope has been limited to long-distance (>100km) trips. The main research question is: Where and how in Europe does, currently and in 2030, the biggest potential of international train passenger travel exist, based on passenger-trip potential (demand) and seating capacity potential (supply)? A framework for potential of the current network is developed based on the passenger-trip potential and seating capacity potential, providing input for a preliminary proposal for a passenger core connections network. The passenger-trip potential is based on the classic 4-step transport model and a gravity based trip distribution including barriers as language and country borders. For the modal split and route assignment a network based on the real available network has been modelled based on direct distance, mode dependant detour factors and average speed. The seating capacity potential assesses the currently provided train connections on their effectively offered seats as the result of the performance on several key level of service indicators: frequency, travel time performance, service level, transfers and offered seats. The preliminary core network is a combination of the potential in seating capacity and passenger-trip potential. It proposes 12 new core connections providing a new international network of train connections with a high service standard. This can improve the international market size of passenger rail travel by 22% in the current situation and even 14x for the growth scenario in 2030. Additionally the amount of CO2-emmission could be reduced with 28 million tonnes