Yggdrasil is an immense ash tree in the centre of the cosmos and connects nine worlds. Odin says that the ash Yggdrasil has three roots that grow in three directions. The Æsir are pictured above Yggdrasil with access to a rainbow bridge (Bifröst) that connects the tree with other worlds.
What then are the Nine Worlds? They are as follows:
Asgard, the home of the Æsir ruled by Odin. The Æsir built it after the homeworld of humans, Midgard and it contains many halls.
Álfheimr the home of the Ljósálfar (Light Elves). High describes the Ljósálfar as "fairer than the sun to look at" in contrast to the Black Elves.
Niðavellir the home of the Svartálfar (Black Elves), also called Dwarves. Hreidmar (a sorcerer) is the king of Niðavellir.
Midgard (Earth), the home of humans.
Jötunheimr, the home of the Jötnar (Giants), descendants of Ymir, and ruled over by Skrýmir. The Jötnar menace the humans in Midgard and the gods in Asgard.
Vanaheim, the home of the Vanir (a group of Gods associated with fertility, wisdom, and the ability to see the future).
Niflheim, a world of ice and snow and the first world to be created after Muspelheim.
Muspelheim, a world of fire and lava. It was when the ice from Niflheim met the flames from Muspelheim that creation began and Ymir was formed.
Hel, the home of the dishonorable dead, ruled by the goddess Hel.