The Caves of Steel by Isaac Asimov (Panther, 1958)

A gift from a friend who knows me far too well:

 

A CRIME THAT COULD INFLAME A GALAXY...

A Spaceman--a specialist in robotics--has been murdered.  Lije Baley, a plain-clothesman of his age, combs the huge cave of steel for a lone fanatic, for a murderer--for the solution to an almost perfect crime.

One of the two men on the cover is a robot—I'm not sure, but I think it is the one who is unconscious.  Don't quote me on that, though!

Isaac Asimov was one of the Big Three names of the "golden age" of science fiction (the others were Arthur C. Clarke and Robert Heinlein).  Asimov is most famous for inventing the Three (fictional) Laws of Robotics:
  

"A robot may not injure a human being or, through inaction, allow a human being to come to harm. A robot must obey orders given it by human beings except where such orders would conflict with the First Law. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law."

 In The Caves of Steel he combines a science fiction novel with a detective story, a combination of genres that for some reason seldom works.  And yet it works in this one.  I put it down to the fact Asimov creates an interesting futuristic setting for his story, then makes it integral to that story rather than using it as window-dressing.  His detectives move through an overcrowded urban world where people huddle under domes and hate and fear the outdoors—and robots.  It's an almost film noir-ish setup—except Asimov was far too prissy and logically-minded to indulge in the sort of sex and violence common in most hardboiled fiction!

Need I add that one of the detectives is a robot and the resolution of this mystery lies in the world outside the domes?

I have another copy of this—also a Panther Book—but alas, it was published in the 1970s, and the cover isn't nearly as interesting.