The Caves of Steel

How do you solve the murder when your new partner is a robot who looks like his creator, the victim?

This is a classic in the Sci-Fi world.  In a far future where the population of Earth lives in huge megas and never see the world outside, the people who have colonized space, the Spacers, have denied Earth's current population the chance to go out and colonize new worlds.  One of these Spacers is murdered, and an Earth detective is assigned to the case.  Now he has to work with a new partner that he can't bring himself to trust.  That partner is a robot, who looks exactly like the victim.  It is both a great mystery, and a fantastic commentary on future over population and our ability to trust robots and artificial intelligence.