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The 3rd International Workshop on Gas-Dynamic Trap-based Fusion Neutron Source (GDT-FNS) was held through the hybrid mode on 13-14 September 2021 in Hefei, China, jointly organized by the Hefei Institutes of Physical Science (HFIPS), Chinese Academy of Sciences (CAS), and the Budker Institute of Nuclear Physics (BINP), Russian Academy of Sciences (RAS). It followed the 1st GDT-FNS Workshop held in November 2018 in Hefei, China, and the 2nd taking place in November 2019 in Novosibirsk, Russian Federation. With the financial support from CAS and China Association for Science and Technology (CAST), this workshop was attended by more than 80 participants representing 20 institutes and universities from seven countries, with oral presentations broadcast via the Zoom conferencing system. Twenty-two presentations were made with topics covering design and key technologies, simulation and experiments, steady-state operation, status of the ALIANCE project, multi applications of neutron sources, and other concepts (Tokamaks, Mirrors, FRC, Plasma Focus, etc). The workshop consensus was made including the establishment of the ALIANCE International Working Group. The next GDT-FNS workshop is planned to be held in May 2022 in Novosibirsk.