
Others have written SF on the theme of immortality, but in The Boat of a Million Years, Poul Anderson made it his own. Early in human history, certain individuals were born who live on, unaging, undying, through the centuries and millenia. We follow them through over 2000 years, up to our time and beyond-to the promise of utopia, and to the challenge of the stars. A milestone in modern science fiction, a New York TimesNotable Book on its first publication in 1989, this is one of a great writer's finest works.
It's about a very small number of people who are immortal, in the sense they stop ageing at 25 (iirc). They can be killed like anyone else, but smaller damages do heal faster. Also, they never get sick. Some are thousands of years old, some less. Some smart, some not so much. How they handle their immortality is very interesting though. I won't spoil it for you though.
[0]: https://en.wikipedia.org/wiki/The_Boat_of_a_Million_Years
1 - Hal Clements _Space Lash_, short story "Raindrop"
2 - L.E. Modesitt, Jr's The Forever Hero trilogy (as well as the "The Mechanic" from Space Lash)
3 - Poul Anderson's _The Boat of a Million Years_
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The story concerns people who are effectively immortal barring death by massive injury. They don't age and often face ostracism or worse by superstitious or resentful neighbours / friends / children. They frequently (re)use the obvious solution - moving on and assuming a new identity - many times over 2000 years of different episodes. However, this becomes untenable and they eventually reveal their identity to a population that is itself becoming long-lived due to improved medical technology.
It's a great read and one of those that illustrates the fact that good SF writers can often write extremely good historical novels. Many of its historical episodes are superb interpretations of periods of history that nowadays aren't particularly well known., e.g. in the post-Roman near east.
[0] https://en.wikipedia.org/wiki/The_Boat_of_a_Million_Years