Time travellers based in our not-too-distant future are researching the past, and two of them, Roy and Lora, are sent to separate parts of the earth in the year 18,862BC, Lora to what will one day be Siberia to live among the mammoth-hunters and Roy, who is our narrator and central character, to Atlantis -- or Athilanta, which is what its natives call it. (Lora never appears in the novel: she is simply the addressee of the series of letters Roy writes that form the text of the novel.)
I've implied that Roy and Lora are time travellers in the ordinary sense. Not so. It's the premise of the book that physical time travel is impossible; instead, folk are sent back in the form of electrical patterns -- clusters of data, if you like -- that lodge undetected in the brain/mind of an inhabitant of the destination era. It is possible for the visiting entity to control the host human being, but not without alerting the host to the traveller's presence, something that's normally to be avoided; Roy gets round this prohibition in order to write his letters to Lora by waiting until his host is asleep, then keeping him in a trance while he does the writing.
And Roy's host is not just any Atlantean: he is Prince Ram (the "Ram" is the generally used short form of an infernally long full name), heir to the throne and already a powerful ruler in his own right. Through Ram's eyes Roy observes the wonders of Atlantean civilization -- and these genuinely are wonders because, contrary to expectations of finding something along the lines of ancient Egypt, Roy discovers a technology roughly at the same level as that of the Victorian era: steamships, electric lighting, etc. In fact, the text irritatingly doesn't give us too many details of the technology beyond what I've just stated, or even much of a description of Atlantean society at all beyond the fact that it has slaves but that these are well treated, and that it has a strong streak of racism toward the primitives of the mainland(s), who are called "dirt people"; instead, the focus is much more on Ram's beliefs and the rituals he must undergo with his father, the king, as he prepares himself to be the fully readied heir to the throne. One of these rituals concerns a star known to the Atlanteans (in translation) as the Romany Star, which presumably means that the concept of gypsyhood was understand long before the emergence of actual gypsies. Hm. Anyway, Roy soon manages to dig out of Ram's mind that the Atlanteans are not in fact humans: they are descendants of the survivors of a startlingly humanoid species whose star swelled up and the usual, who sent off a pitifully few colonists in quest of a new home amid the myriad stars of the Galaxy, etc., etc. Clearly the Atlanteans have not been able to build up their technology to anything like the levels they once enjoyed, but they've done the best they can with the limited resources available to them here on earth. Their racism is still pretty repulsive, but more understandable (according to the text) once we realize that humans are actually a different and less developed species.
Eventually Ram detects Roy's presence, regarding him as a possessing demon. Even when Roy, recognizing the inevitable, breaks every rule in the chronic argonaut's rulebook and "introduces himself" -- explains he is a historian from the far future and ya-de-yada -- Ram still regards him as some kind of wizard. And here, I think, the machinery of the book creaks down. If the Atlanteans are indeed the relics of hi-tech spacefarers, how come their minds are still polluted with all these stupid superstitions? It's not just the belief in demonic possession and wizards (and, for that matter, in the moral acceptability of slavery): the Atlanteans also worship a whole pantheon of gods who seem to have attributes akin to those of Olympus. Surely we might expect an advanced culture, even if it had perforce regressed technologically, to have grown out of this sort of stuff? I'm not making an anti-religious point here (for once); what I'm saying, rather, is that we're being expected to believe in a culture that's composed of cultural elements that simply don't go together -- that are chalk and cheese.
Letters from Atlantis is nicely enough told, but it's a slight work (I think it was intended as a YA novel, which is no excuse; I've read it as part of Silverberg's three-novel Cronos omnibus, hence the uncertainty) and, as I say, doesn't seem really to hold together.