By Robert A. Heinlein.
This is the same dustjacket design as on the first-edition hardcover, and my copy is in fact a first edition—but an umpteenth printing, and not collectible at all.
This book is a Hugo winner. It's by science fiction's greatest author. The current Tor hardcover and trade paper editions have an utterly gorgeous cover, too.
None of which is the point. The point is—well, why is this book so good? Lots of reasons, of course. I found it tremendously enlightening about subjects ranging from monogamy to how to run a revolution to artificial intelligence to libertarian society. We got to watch a good man be politicized—and stay a good man. There were at least three first-rate central characters, and a round dozen of good supporting players. And they all worked together and didn't get in each other's way.
Remember the moment of insight when Mike pointed out that they could "throw rocks" at Earth? Remember the problems of fighting downwards in unfamiliar gravity? Remember Mike's solution to the problem of betting on horse races? Remember how Manny met Stu? Remember the first Lunar elections? There's a lot of stuff worth remembering in this book (and I'm sure your favorite bits aren't all the same as mine).
Yes, the computer technology is a bit quaint. "Tubs of random numbers" was quaint when I first read it (whenever that was; probably not too long after it came out in 1965/66, though I definitely didn't read the magazine serial). The monster central mainframe wasn't quaint (then), though as Heinlein pointed out it was stupid for life-critical engineering controls. Insights into little things remained good, though—Mike wasn't "on" the phone system (until Manny put in a connection), even though he controlled it.
I think this is Heinlein's most aggressive playing with language. The Lunar dialect of English makes pretty good sense to me (though I'm not a linguist) given the history he gives it (Australian and Russian words dominate the departures from current English). This is one of three books I remember with a thoroughgoing made-up dialect (the others being Anthony Burgess' A Clockwork Orange and David R. Palmer's Emergence), and it's far and away my favorite.