The Necromancer, who actually was the Dark Lord Sauron in hiding before he reentered Mordor.
While this did help the health of Mirkwood some, its main effect was to cause Sauron to actually return to Mordor and call up his servants the Nazgul.
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As Gandalf said, it would take weeks and weeks of trekking out of their way to go around Mirkwood. Hundreds of miles out of their way. It would be much too bothersome and time-consuming, rather than just cutting straight through it.It was too long of a trip and it would have taken them past Dol Guldur to the south and orcs or dragons to the north.
Gandalf's first action in The Hobbit is to show up on Bilbo's doorstep, and get invited for tea. He shows up a bit late, having told a few dwarves looking for a burgler to stop by as well. These dwarves, at Gandalf's advice, hire Bilbo for the position. Gandalf then accompanies them for a part of their journey. While with the dwarves and Bilbo, he saves them from three angry trolls and rescues them from the goblins of the mountains. With this accomplished, and the dwarves well on their way to their destination, Gandalf leaves them to go do something else that needs doing. Gandalf left the dwarves, in fact, to go and deal with an evil power growing in the south of Mirkwood Forest. This power is referred to as the Necromancer in The Hobbit, and turns out in the sequel to be the dark lord Sauron, who held Middle Earth in terror for a thousand years. Gandalf, and a few wizard friends, successfully drives the Necromancer/Sauron from Mirkwood. Since their foe simply pretended to flee and then sent a few henchmen to take it back, the action wasn't really all that useful, but it's the thought that counts. This done, Gandalf returns to the dwarves, and is there in time to warn them of an approaching goblin army. After the goblins are defeated, Gandalf guides Bilbo the hobbit back home, and goes off to do whatever wizards do.
Mirkwood is a deep, very large forest. It is populated by nasty creatures that peer out with large eyes at night. There is nothing there that can be eaten. Sunlight does not penetrate through the heavy foliage.
He did not abandon the Dwarves in Mirkwood. He had to help handle the problem of the Necromancer in the south part of Mirkwood. This was necessary because, when he had infiltrated the Necromancer's fortress, Dol Guldur, and found Thorin's father, he had found out that the Necromancer was indeed the Dark Lord Sauron, taking shape again.Gandalf, along with the rest of the White Council, were afraid that Sauron would take notice of the great Dragon living just to the East of his fortress and form an alliance with Smaug, who was, perhaps, the last of the Dragons with the old fire. And so, while the Dwarves and Bilbo dealt with Smaug, Gandalf and others of the White Council attacked Dol Guldur, only to find that Sauron had fled (presumably back to Mordor, since that is where he is in LOTR).
His known names, usually given to him by various peoples: -Gandalf ("Elf of the Wand", though he is not an elf) by various peoples. Titled as "Gandalf the Grey" and "Greyhame" or later "Gandalf the White". -Mithrandir (Sindarin "Grey Pilgrim", "Grey Wanderer") from the Elves, also used by the Men of Gondor. -Tharkûn, from the Dwarves. -Incánus, from somewhere in the South. -Olórin, which he was called in the West in Aman. He has also been called various other things, some of therm derogatory, although they are not used as proper names.