The dawn of space travel and now space tourism has led to legal questions concerning the Moon and given law geographers something else to talk about. The space faring countries of the United States, Russia, China, and others who have not sent people into the heavens have signed the Outer Space Treaty which treats the Moon like international waters. No one can claim it but everyone can use it. Another treaty known as the Moon Treaty sought to limit resource extraction but the treaty has not been signed by any major space power.
So right now the Moon is open to all sorts of activities. People like Dennis Hope make a living off scamming people claiming to own the Moon. Hope claims the Outer Space Treaty only prevents countries from owning the Moon and not people. This is only a half truth and the international waters analogy has to be used again to make things clear. Any private person or group can access resources in international waters. However, no one can own the resource while not directly utilizing them. So it is open season. If Hope is not on "his property" with a shotgun there is nothing stopping Catholicgauze offering Bishop of the Moon property titles to anyone who wants it. So unless you are willing to homestead, avoid buying moon property. The same goes for those who claim to own property on other planets or name stars for a fee.
The Moon and space are free (you just have to pay millions to get there).