The stories of I, Robot - and Asimov's robot stories in general - tend to circle around two central themes:
- Humanity's control and understanding of the technology it has created.
- Non-human life, and the capacity of life which simulates humanity to feel and be human.
These two themes are in tension with each other, which is part of what makes them such a rich, powerful pairing.
Controlling and Understanding Our Technology
Many of Asimov's robot stories revolve around the Three Laws of Robotics, which are meant to be defining boundaries and keep robots' behavior predictable and nonharmful. And in many of the stories, something goes wrong -- the robots do not behave as expected; an interaction between the Laws arises which is not expected; the Laws turn out to have consequences that were not expected; etc., etc.
As many iconic SF stories do, Asimov posits consequences that are always purely logical. The initial premise of beings following the Three Laws is entirely logical and abstract, and great importance is always placed on the fact that the results - surprising and unexpected though they may be - flow logically from the premise, given the right circumstances.
And so the question that remains, that the stories interrogate, is: Are humans clever enough, wise enough, logical enough, to anticipate all the consequences of the technology they build? Can we deal with what we have created, or are we going to fall into a trap of our own making?
Different stories deal with this in different ways - from Liar!, where Susan Calvin realizes that the consequences of the Laws force a robot to lie and distort reality in order to avoid causing her pain, to The Evitable Conflict, where humanity realizes that robots, in following their rules, have plucked away humanity's agency entirely.
The Humanity of Robots
Many of the stories anthropomorphize and personify the robots -- portraying them as not only machines, but actually capable of emotion, which is effectively as real as our own. This gives rise to a slew of questions about what being "human" truly means -- and if it can be artificially simulated, what does that mean?
Robbie is very clearly in this vein, where Gloria realizes she cannot think of him as anything but an individual. Little Lost Robot toys with the idea of a robot gaining a superiority complex, wanting to prove itself "better" than a human. And so on.
Together, the two themes are extremely intriguing, because they are in tension with another. If robots are, in some way, human, they cannot be anticipated and controlled. And to the extent that they follow logic to whatever conclusion it lead them, then they are clearly something other than human.
There are many ways for these themes to conflict and interact. One example is Reason, where a robot believes he is a prophet, and comes up with bizarre, mystical explanations for the world it observes. Clearly, this robot is behaving irrationally, and in some ways in a very human way -- but the protagonists observe it is still following the Three Laws, so it is being both robotic and human at the same time. This, of course, hints at what further tension could develop if the robot's irrational, human-like beliefs didn't happen to dovetail so nicely with what the humans wanted the robots to do anyway.