Despite the Apollo landings in the 1960s, there are many unanswered questions about the moon that could be researched with the aid of permanent space stations. For example, some scientists still believe that there could be frozen water underneath the moon's surface. Also, the moon was likely originally part of the Earth during the initial stages of the solar system, and studies could be done to conclusively prove this as true and, if proven true, this would give scientists a better glimpse into how the solar system was formed.
The moon's lower gravity and relative lack of an atmosphere could allow for experiments that could not be performed on Earth. For example, the moon is an ideal location for the placement of telescopes because scientists do not have to contend with the Earth's atmosphere.Large sections of the moon are effectively unexplored by astronauts and astronomers; permanent moon bases would allow scientists to explore these undiscovered areas without having to worry about a time table for returning.
Space stations on the moon would also allow astronauts to acclimate themselves to living on a non-Earth surface, which would be essential if they were to explore beyond the moon. The next most likely location for astronauts to visit is Mars, but that trip alone takes years. Thus, if astronauts go, they would want to stay on the surface of Mars for a long period of time to make their travels worthwhile. Moon bases would allow astronauts to prepare for circumstances they would encounter on Mars with the relative safety of being able to return to Earth in three days time.
Besides advantages for science, there are also pragmatic reasons for considering a space station on the moon. At the current rate of population growth, it is inevitable that at some point in the distant future the human species will simply run out of places to live; space stations on the moon could help alleviate the pressures of overpopulation. Additionally, because of its almost complete lack of atmosphere and relatively stable geological conditions, the moon would be a safe place to store an archive of human history.