(wow, that title…)
Two works of SF set on our satellite:
Luna - a series by Ian McDonald
The series comes to a satisfying, if slightly rushed, conclusion. The fact that maybe 80% of the female character’s names start with A doesn’t really help, nor does the sudden introduction of a fourth major faction (the University on Farside) feel very organic.
The Moon is a Harsh Mistress by Robert Heinlein
I think the influence from this book on McDonald’s work is pretty obvious. Both feature a Luna that’s used for extracting resources for Earth, both feature a future libertarian society, and both feature the move towards independence.
Of course, Luna is written 40 years after The Moon… , and instead the Moon’s inhabitants being convicts from an authoritarian Earth, the ones in Luna are the ultimate gig workers. They take out loans to finance the trip, and pay for the “4 basics” - air, water, carbon and data. Don’t have enough to cover those? You will die and your mass reclaimed.
I find Heinlein’s view of women retrograde and borderline misogynistic. He gets points for imagining a future melange of languages, the libertarian quasi-utopian is as (im)plausible as McDonald’s, and the depiction of “Adam Selene”, the friendly AI that helps with the independence is well written.
One big difference is that in RHA’s work, libertarianism is an utopia, in Luna it’s a nightmare.
 Although Charles Stross has tweeted that the helium economy in Luna makes no scientific sense, the idea that it would be economical to grow wheat on the Moon and send the produce to Earth, as in TMiaHM is even dumber.
 in the “original” there are no laws, only contracts sense.