The great forest formerly called Greenwood the Great is Mirkwood in J.R.R. Tolkien’s legendarium.
Greenwood the Great was a major woodland in the north-east of Middle-earth. After the rise of the Necromancer, who was secretly Sauron, a shadow spread through the forest and it became known as Mirkwood.
The forest appears prominently in The Hobbit. Bilbo and the dwarves cross it during their journey to the Lonely Mountain, encountering giant spiders and the Elvenking’s realm. Its dangers make the route far more than a simple woodland passage.
Mirkwood should not be confused with Fangorn Forest, where the Ents live, or Lothlórien, the woodland realm of Galadriel and Celeborn. Those forests have distinct locations, peoples, and histories within Tolkien’s geography.