What are some of the local stories of myth that are popular in Iceland that are often told within Iceland literature are recited by Iceland children?
Huldufólk the Iceland elves, the name mean hidden people because they can become invisible to people, they have larger build, wearing only grey clothes, and they have black hair, and they also dwell in mounds, to know that they are elves or differentiating between them and human when they show themselves are the latter have a convex rather than concave philtrum below their noses.
Due to their tendency to remain invisible, many Iceland folktales give a caution to not throwing stones randomly so it won't hit this elves.
Iceland's storytelling tradition is quite rich, full of tales about ghosts, elves, etc. Is quite rich. Check the stories at the bottom of this page out:
Source 9k
The fourth one is especially famous.