The nine worlds are the divisions of the cosmos in Norse mythology, connected by the world tree Yggdrasil. The number is given in the sources, the Voluspa speaks of nine worlds and of nine roots or supports of the tree, and Vafthrudnismal refers to nine worlds, but no surviving medieval text supplies a list of all nine, and this is the central difficulty in any discussion of them.
The names that do appear in the Poetic Edda and in Snorri Sturluson's Prose Edda include Asgard, home of the Aesir; Vanaheim, of the Vanir; Midgard, the enclosure of humans; Jotunheim, of the giants; Alfheim, of the light elves; Svartalfheim or Nidavellir, associated with dark elves and with dwarfs; Niflheim, the world of mist; Muspelheim, of fire; and Hel, the realm of the dead. The standard list now in circulation is assembled from these, but the sources do not agree on which belong to the count, whether Svartalfheim and Nidavellir are one place or two, or whether Hel is a world in its own right or a region within Niflheim.
Two cautions are important. Snorri wrote in thirteenth-century Iceland, more than two centuries after the conversion, and his systematising has repeatedly been shown to impose more order, and in places more Christian and classical framing, than the older poetry will support. And the poems themselves are of varying date and provenance and were not composed as a system in the first place. Scholars therefore generally treat Norse cosmology as a set of overlapping traditions rather than as a map, and are notably cautious about the tidy nine-realm diagrams now widely reproduced, almost all of which derive from nineteenth- and twentieth-century reconstructions and, more recently, from popular culture rather than from the medieval texts.
What is well attested is the structure rather than the enumeration: a tree at the centre, worlds arranged in relation to it, humans within a middle enclosure with hostile powers outside it, and an underworld beneath. The number nine recurs throughout the Norse material for its own sake, nine nights of Odin's hanging on the tree, nine daughters of the sea god, nine steps taken by Thor after killing the serpent, and it may be that the number carries significance independently of any definite roster of realms, which would be the simpler explanation of the discrepancy.