Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
First Person (Central Narrator)
Kris Kelvin is the guy who's telling you the story, and he's also the main character. You can't get out of his head—which is a central theme in the story. Solaris is about being confronted with the contents of your skull, and about how you can't ever get out of that skull, so everything is ultimately unknowable.
Kelvin's not particularly reliable or forthcoming as far as narrator's go (how much do we find out about Rheya anyway?), but again, that's the point. You're trapped in there with him—or as the man himself says:
I was going around in circles; there seemed to be no escape. It was not possible to think except with one's brain, no one could stand outside himself in order to check the functioning of his inner processes. (4.95)
Welcome to Kelvin's brain.