The Lunar Gravitational-wave Antenna (LGWA) is a mission conceived as a network of stations to measure the vibrations of the Moon caused by gravitational waves (GWs). The long-term vision is to accomplish ground-breaking, paradigm shifting science in the coming decades on the Moon. LGWA will lead to the first observation of GW signals in the decihertz band greatly expanding our understanding of the universe and laying out a path to eventually probe the moment of its creation. LGWA stations will also be unique contributions to a lunar geophysical network shedding light on the Moon’s formation history. LGWA is a project of inclusion and international collaboration, where space-faring and space-aspiring nations can contribute to the LGWA network with their own stations whose cost depends on the targeted station lifetime and deployment location. With respect to the baseline concept proposed here, different sensor technologies can be implemented over time with the goal to continually increase the performance of the LGWA network. The broader context of lunar GW detection and its long-term vision are outlined in an accompanying topical white paper.