How we cite our quotes: (Chapter.Paragraph) Note that chapters aren't numbered, so need to be numbered manually, 1 to 14.
Quote #1
For a fraction of a second, my throat tightened and I thought longingly of the Prometheus and its strict discipline; the memory of an existence which suddenly seemed a happy one, now gone forever. (1.67)
Kelvin has barely landed on Solaris, and he's already nostalgic for the lost past of being on a spaceship and having people tell him what to do. This is not a forward-looking, no-regrets kind of guy.
Quote #2
But evidently the dead do not change; they remain eternally young. (5.5)
This could be a comment on the afterlife, but it could also be a comment on how memory works by freezing people in time. And you could also say that memory has frozen Kelvin himself in time; he can't get past Rheya's memory (and we know this is true, because the magic ocean told us so).
Quote #3
I leaned over her and turned back the short sleeve of her dress. There, just above her vaccination scar, was a red dot, the mark of a hypodermic needle. I was not really surprised, but my heart gave a lurch. (5.35)
This is a creepy bit of business. Rheya has the mark of the needle that she used to kill herself. Kelvin's memory of her is also the memory of her death; the two can't be separated out.
Quote #4
"I have the feeling that I've forgotten something," she went on, "that I've forgotten a lot of things. I can only remember you. I… I can't remember anything else." (5.68)
Kelvin's memory of Rheya's memory is not what it should be: She only remembers him. And since he thought her up, you could see this as meaning he only wants her to remember him. Welcome to the Kelvin show.
Quote #5
"No," she said at last, "be quiet, don't talk like that. It's no good, you're not the same person any more." I started to protest, but she went on: "No, you don't want me." (8.13)
You could understand this as Rheya recognizing that something really weird is going on (like she's some sort of phantom projection made of neutrinos, for example), but you could also see it as Kelvin running through fairly standard-issue relationship-falling-apart conversations from his past. It seems possible that Kelvin and Rheya have had this exact dreary discussion before. They're doomed to repeat their breakup over and over inside Kelvin's head.
Quote #6
"It… it didn't work," she stammered. "Why are you looking at me like that?" Then she screamed out loud: "Why are you looking at me like that?" (9.123)
This is what Rheya says after she drinks liquid oxygen and then regenerates. She keeps trying to get rid of herself and keeps coming back, like a memory you can't forget.
Quote #7
"Then who are you?"
There was a long silence. Then she bowed her head and murmured:
"Rheya… But I know that I am not the woman you once loved."
"Yes. But that was a long time ago. The past does not exist, but you do, here and now. Don't you see. " (9.145-148)
The real Rheya's gone, the fake memory Rheya is still around. So does that mean the memory of Rheya is the most important thing? It doesn't seem like it should. But Kelvin is under a lot of stress, admittedly.
Quote #8
"Now all I see is you." (9.186)
Again, you could see this as being kind of sweet (he loves this Rheya so much he's forgotten her prototype)… Or you could see it as kind of icky and sad—the memory of Rheya has completely erased the real Rheya, so now he's just in love with his own projection, not with the real woman.
Quote #9
"Who do you want to save? Yourself? Her? And which version of her? This one or that one? Haven't you got the guts to face them both?" (10.81)
Snow says "which version of her," in reference to the first and Rheyas who showed. But it could also mean the memory of Rheya or the real Rheya, or perhaps all the different memories of Rheya. Anyway, the answer to Snow's final question is clear enough: Kelvin does not have the guts to face them both. Guts are not his thing.
Quote #10
[…] I was finally no longer able to tell which of them was looking at me, my father or Giese. They were dead, and neither of them buried, but then deaths without burial are not uncommon in our time. (11.25)
This is an odd passage, in which Kelvin's father (whom we know nothing about) and Giese (whom we don't know much about) blur into each other; a doubled, ill-defined ghost, to go along with all the other doubled ghosts Kelvin is keeping around himself. The line about the commonness of deaths without burial seems like it could refer to memory itself and the fact that, for Kelvin, people don't die and go away; they just stick around in his head.