The Redaction Machine is a sci-fi story about the invention of a machine which can immediately reverse a person back to a past self, keeping only selected memories on the way. This, of course, grants immortality of a sort.
The story follows Jane, a woman from the 21st Century, who becomes one of the oldest people in the universe as the story progresses, and explores the effects of both the technology (effective memory wiping) and immortality on the main characters and humanity as a whole.