The Naked Sun   by Isaac Asimov

However, by the time you get to the end of the book a brilliant murder-mystery will have unfolded, a small handful of wonderful personalities will have been exposed to you, and then some profound thoughts on the future of mankind are manifested. And after all, it was not a robot who committed the murder, but a woman who the detective susses but lets go (she is not the real villain). All twists and turns which follow logically from one another yet are completely unpredictable.

And the story: an earthman who has never seen the sun and is agoraphobic is summoned to investigate a murder on a planet where people never see each other directly, and are violently homophobic. He is accompanied by a robot from a third planet, who poses as a real human (the detective is able to blackmail the robot into keeping out of the way by threatening to blow its cover). During his investigation he sees the planet's chief detective poisoned in front of him, and reasons that the robot that served the drink had been conned into breaking the laws of robotics. He meets a woman who looks after children, and a man who is the planet's chief roboticist, both of whom were intimately connected with the original murder victim. It transpires that the woman killed her husband by clubbing him with the detachable arm of a robot that the roboticist supplied. The woman was trying to find love on a planet of zero contact, and the roboticist was trying to take over the world and beyond. Both get their just desserts.

And after it all, the earth-based detective concludes that it is wrong for the human race to remain underground, but must get out and explore the stars for its own sake.