One short story on the list, which is dominated by movies and television:
"The Man Who Evolved" by Edmond HamiltonRead about the other entries on the list.
A lot of stories deal with the idea of individuals "evolving" themselves, which is pretty much just nonsense. Evolution is a species-wide phenomenon, not something an individual does. An individual can mutate yes - indeed, everybody features some genetic mutation or another, but most are so minor and unimportant that nobody actually recognizes their particular little mutation. We are all, in our way, mutants, and humans, as a species, are constantly evolving, but that doesn't mean a human can evolve.
Still, the notion of a person mutating him or herself along humanity's supposed evolutionary path is a great premise for a science fiction story, even it's pretty much nonsense. Edmond Hamilton's 1931 short story is one of the first and most famous tales to use this idea, as mad scientist Dr. John Pollard claims he's focused cosmic rays to accelerate an individual's evolution at a rate of 50 million years every fifteen minutes.
Pollard then undergoes many blasts of evolution, each time emerging with a more advanced mind and a frailer body. Eventually, he becomes nothing more than a free-floating, telepathic brain that consumes pure energy. One last evolutionary blast turns him back into a protoplasm, Earth's original life-form, suggesting that evolution is somehow cyclical. It's a clever twist, and no less than Isaac Asimov said it was the first science fiction short story that really stuck with him, but the idea of cyclical evolution is almost as silly as a person hyper-evolving himself with focused cosmic rays.