There are nine realms in the Norse mythological universe, each inhabited by a different type of being. They are held together by Yggdrasil, the Tree Of Life, a giant ash tree which reaches from the heavens to the netherworld. Yggdrasil has three roots, one for each part of the universe.

Asgard

This is one of the heavenly realms, surrounded by a high stone wall. It is the home of the Aesir, a group of warrior gods and goddesses headed by Odin and his wife Frigg. The most well-known deities of this group are Balder, Thor, Loki, and Freya.

Part of Asgard is the plain of Idavoll, the location of the halls of Gladsheim and Vingolf, where the gods and goddesses meet to discuss the fate of the world and other important topics. Asgard also contains the Well of Fate, located underneath Yggdrasil’s upper root.

Vanaheim

Home of the Vanir, nature and fertility deities, Vanaheim is also one of the heavenly realms. Aesir and Vanir were enemies for a long time, but eventually made peace. Hostages were exchanged, and ultimately the two groups of deities became one.

Alfheim

Alfheim is the third of the realms of the upper reaches. The elves of light live in this area. They do not participate in the affairs of gods or men, preferring to keep to themselves.

Valhalla

Although this enormous hall is not considered a realm, it is also part of the heavens. It is a place of feasting, where dead human warriors killed in battle wait until the day they will fight at the side of the gods at Ragnarok, the end of the world.

Midgard

This is a giant fortress the gods built for humankind to protect them from the giants. It is part of the middle section of the universe.

Svartalfheim

The second of the middle realms belongs to the dark elves. Just as their light cousins, the dark elves do not concern themselves with the rest of the world.

Nidavellir

Also located in the middle part of the universe, Nidavillir belongs to the dwarfs. The dwarfs interact with humans and gods, mostly in the capacity of craftsmen.

Jotunheim

This last of the middle earth realms houses the frost and rock giants. It is also home to the Well of Wisdom, located beneath the middle root of Yggdrasil.

Niflheim

This is a cold and icy region at the bottom of the universe. It contains Nastrond (Shore Of Corpses), home to Nidhogg, a serpent or dragon who eats corpses and gnaws on the roots of the world tree. The spring Hvergelmir is also located in this area, underneath Yggdrasil’s lower root.

Helheim

Located in Niflheim, Helheim is the region of the dead, completely surrounded by the river Gjoll, which originates at the spring Hvergelmir. It is reserved for those humans who die of old age or disease and for warriors who are not killed in battle.

Muspell

This area belongs to the fire giants. It is not considered one of the realms of the universe.

Ginnungagap

Also not part of the universe, this is the Void of Chaos, located between Niflheim and Muspell. Life was first created in this area, when ice from Niflheim and hot air from Muspell met.

Sources:
Godchecker.com at http://www.godchecker.com
Encyclopedia Mythica at http://www.pantheon.org