THE CAVES OF STEEL – ISAAC ASIMOV

a science fiction detective novel set in a futuristic world where humans live in both underground cities and in space colonies. The story revolves around Detective Elijah Baley, who is assigned to investigate the murder of a Spacer, a colonist from one of the outer worlds, and is forced to partner with a robot, R. Daneel Olivaw, to solve the case.
Now Baley and Olivaw are faced with two clear impossibilities: Either the Solarian was killed by one of his robots—unthinkable under the laws of Robotics—or he was killed by the woman who loved him so much that she never came into his presence!