As I mentioned in my general Asimov post, a common accusation towards Asimov was that he didn't really write characters, but more shaped pieces to support his plots or story ideas. In general, this is a fairly accurate descrition, though it's not exactly a negative thing; much of what Asimov wrote didn't need characters as such, because many of his stories were stories of ideas – ranging from SF stories that were nothing but a setup for a bad pun to what-ifs to mysteries based on logic which wouldn't vary much no matter which person you put into the various slots of the puzzle.
At the same time, in a few of his works Isaac Asimov demonstrated that he could, if he wished, write stories which did include characters, and ones whose behavior, thoughts, and actions were significant to the plot. Of these, the best best are those generally called simply "the Robot novels". In my view (and that of, in my experience, most fans) the first two of these, The Caves of Steel and The Naked Sun, are the best, with The Robots of Dawn not being terribly bad and Robots and Empire being the least of them (partly because it was another component of his attempt to unify the Foundation and Robot universes, something I never liked) -- apparently others agree there, because there appears to be no Kindle version of that novel and no current-in-print version.
The Caves of Steel takes place in what is, in some ways, a quintessential 1950s future, where humanity's urbanization has reached its peak; virtually all the inhabitants of Earth live in the vast Cities which are completely enclosed megaplexes, gargantuan arcologies before the word "arcology" was ever imagined. The Cities are self-sufficient, self-powered, ordered and safe, the ultimate extrapolation of the New York City of Asimov's own youth.
But things are not perfect in the Cities. The middle-class still struggles, jobs are still competed for, and there are other, more complex problems; the Spacers – humans who are natives of other settled worlds, once Earthly colonies but ones who have severed all ties centuries ago – are pressuring Earth to change her ways, including allowing robotic labor to take a greater and greater part in the operation of the Cities; since the workers of the Cities fear being displaced from their jobs, there is much hostility and resistance to the idea.
Into the middle of this comes Elijah Baley, Plainclothesman C-5 of the New York City Police Department. Baley is a classic "good cop" – he takes his job seriously and tries to do his best, and while he certainly appreciates perks in his job, is more interested in doing his job right than in angling for promotion. He's reliable and loyal to the department, and has a good record… all of which make him the perfect choice for his boss, Commissioner Julius Enderby, to assign to a particularly sticky case: discover who murdered a Spacer, Roj Sarton, in their own compound, while assisted by a Spacer investigator, Daneel Olivaw.
An investigator who just happens to be a robot, his full name being R. Daneel Olivaw – Robot Daneel Olivaw.
Baley has no more reason to love or trust robots than anyone else in the City, and Daneel turns out to be in someways worse. Daneel Olivaw is a perfect humaniform robot – he appears human in every possible detail, and as a near perfect human specimen: tall, bronzed-tanned, perfect features and so on, making Baley feel plain. As a robot, Daneel has all the obvious advantages; he is vastly stronger than a human, tougher, faster, and as an investigator would seem nigh-perfect. A robot never forgets anything, a robot never misses any detail at a scene, a robot can often sense things humans cannot, and can make impeccable logical analyses.
But Daneel is also restrained by the Three Laws of Robotics; while he has some latitude programmed into him for practical applications (and with far better conceptualization capabilities than most Earth robots are ever allowed), he still must follow the basic dictates:
First Law: A robot may not harm, nor through inaction allow to come to harm, a human being.
Second Law: A robot must obey the orders of a human being, except where those orders would conflict with the First Law;
Third Law: A robot must act to protect its existence, except where that action would conflict with the First or Second Laws.
Elijah Baley must somehow discover who murdered Dr. Roj Sarton, and why; he must do so himself, without letting Daneel Olivaw upstage him, or he will prove that a robot investigator is superior to a human one; and he must do all this without triggering an interplanetary incident that may involve the now-insular and weakened Earth in a conflict with the powerful and capricious Spacers!
Baley's journey is a very emotional one, and absolutely determined by his personality as a character. We often see his moments of uncertainty, insecurity, and – in a couple of cases – complete personal humiliation and embarrassment, when he thinks he has the solution and turns out to be utterly wrong. We see his marriage – not an entirely happy one, but not entirely unhappy, either – and his attempts to keep a family life despite the limits of City life.
But at the same time, we see that he is a genuinely good man, who will not allow his prejudices to keep him from doing what is right. We see him gradually warm towards Daneel, and his own presence and behavior changes Daneel in subtle but unmistakable ways. To a considerable extent, even though Baley is far more flawed than James Kirk, their relationship very strongly foreshadows that of Captain Kirk and Mr. Spock; Daneel and Spock are in some ways startlingly similar.
Baley is also tenacious and unwavering in his pursuit of justice – to the point that he even ends up instructing Daneel in the difference between justice and law. Despite failing to uncover the murderer quickly, and multiple barriers thrown in his way, Elijah Baley presses on, even finding technicalities at the last minute to keep himself on the case even though he has been removed, and – as we might expect – does finally track down the killer in a brilliant last-minute gambit that manages to resolve the entire problem in a way that everyone – even the murderer! – can accept.
The Caves of Steel is one of my absolute favorite Asimov novels, and allowing for the passage of time still holds up pretty well. One amusing part of its background is that the "virtually unsustainable" population of Earth, which required the creation of the Cities and the nourishment of most people on yeast-based creations rather than any regular food, was the staggering number of…
… eight billion. By comparison, we're well over seven billion today. Estimates of how many human beings could be supported on Earth by various approaches vary, but I've seen believable estimates in the trillions. As with so many things, the time at which something is written heavily influences what it assumes. This is not much different from the old SF novels that describe the immense storage capacity of the supercomputer in megabytes.
If you've never tried an Asimov novel, this is one of the ones I recommend most highly.