Yep, that's the actual edition I own over there on your right. Cost me a whopping 95¢ back in 1968 or so. Currently out of stock at Amazon, but the in-print paperback goes for $15.99. (Kindle version only $12.99.) It's probably one of those books that set me on my current cranky-libertarian ideological hobby-horse. Thanks, Bob! And it also won the Hugo for best SF novel.
And this leaves 17 books to go on my reread-Heinlein project. Wish me luck, I think I'll need it.
The narrator here is Mannie O'Kelly-Davis, computer technologist on the Moon. One day he discovers that the large computer he's been maintaining has crossed the threshold into sentience. Cool! Mannie keeps this a secret, dubs his AI friend "Mycroft" (Mike for short), and together they arrange for periodic glitches so they can get together and chat. (Yes, Mike can converse. Not surprising in this day of Alexa/Siri/Cortana. Big deal when the book was written.)
The late 21st-century Moon is a penal colony, inhabited by a few million prisoners, and their descendants, ruled by the Earth-appointed "Warden" and his "Lunar Authority" thugs. Luna is also an exporter of lunar-grown grain to Earth. (Not the most stable of situations, and the economics are suspect, but go with it.) Always-curious Mike asks Mannie to go to an anti-government meeting, where gripes are aired, the thugs crack down, violence occurs. Mannie barely escapes with beautiful Wyoming Knott, and Professor Bernardo de la Paz; both are well-known agitators.
Mannie gets roped into an unlikely scheme to throw off the shackles of Earth domination, and establish an independent Luna. Even more unlikely (or is it?), Mike joins them as an ally. We are taken into the nuts and bolts of revolution of the plucky downtrodden against oppressors with vastly more resources at their disposal. Heinlein obviously thought a lot about the details here.
I think Heinlein was the first writer to speculate on computers becoming conscious. (Although Asimov's R. Daneel Olivaw was pretty close.) It's pretty much a staple these days, but I think it was mind-blowing at the time.