The Nine Realms
Álfheimr, home of the good elves is above Muspelheim.
Asgard, also known as Godheim, home of the Æsir gods, ruled by Odin and Frigg. There are twelve Æsir (with the exception being Loki, a giant, Njörðr and Freyr, originally of the Vanir) and fourteen Asynjur (goddesses) (with the exception of Freyja, originally of the Vanir).
Jötunheimr, home of the giants. The giants are constantly at war with the Æsir. The Jötunn have many leaders and strongholds within their world. The most notable are Thrymheim, the abode of Thiazi, his brothers Gangr and Idi, their father Olvaldi and the original home of Thiazi's daughter Skadi, who later joins the Asynjur.
Midgard, or Manheim, home of humans. The Æsir sometimes visit upon the Bifröst bridge (a rainbow). Midgard is located below Asgard.
Muspellheim, home of the Fire Giants. They are lead by Surtr, who is destined to kill the god Freyr and engulf the world in flames. Muspellheim is the southernmost of the realms.
Niðavellir is one of the Nine Realms of Norse cosmology. It is the realm of the Dwarves. Hreidmar is the king of Niðavellir.
Niflheim, home of the dishonored dead and is ruled by Hel, daughter of Loki, who is described as having half her body alive and the other half a rotting corpse. Only the dead who die in sleep of cowardly (not in battle) end up here. It is the home of the Niddhog, a dragon who eats at the roots of the tree that bind it.
Svartálfar (meaning home of the svart alfs or black elves) is the abode of the dark elves, or svartalfar. The Svartalfar are masters of metalworking. Two of their number, Brokk and Eitri (collectively known as the sons of Ivaldi) made magnificent gifts for the gods, for Freyr, Skidbaldnir (Freyr's ship, that may be folded into hsi pocket when not in use), Gullinbursti (a golden boar), for Odin, Draupnir (a magic golden ring that duplicates by eight itelf every nine nights) and Gungnir (a magic spear), for Sif a new wig of gold (after Loki cut off her real hair) and Mjölnir the Hammer for Thor. The chains that bound the legendary Fenrir were also forged in Svartálfar.
Vanaheimr, home of the Vanir gods, associated with wisdom, fertility and the future. Vanaheimr is the original home of Kvasir, Njörðr, Freyr and Freyja. Vanaheimr is located above Alfheim. The Æsir and Vanir go to war, with the result being the swapping of Kvasir, Njörðr, Freyr and Freyja of the Vanir with Hœnir and Mímir of the Æsir.