In Norse mythology, Álfheim ("world of the Elves", "land of the Elves" in Old Norse), Alfheim, Ljösalfheim, or even Lightalfheim designates two distinct places: one of the nine worlds or the home of the Vanir God Freyr.
The Poetic Edda (Grímnismál, 5) relates that the gods gave Freyr the gift of Álfheim when he cut his first tooth, according to a custom still alive in Iceland (tann-fé). This version, however, contradicts the myth of the war between Aesir and the Vanir, at the end of which Freyr plays a role, presumably as an adult.
In Snorri's Edda (Gylfaginning, 17), Álfheim, on the other hand, is the residence of the Lights Elves.
Despite the identity of the names, there is no known relationship between Freyr and the Elves.