The wizard who guides Bilbo Baggins and the dwarves in The Hobbit is Gandalf.
Gandalf visits Bilbo at Bag End and helps organize the quest to reclaim the Lonely Mountain from Smaug. He brings Bilbo into the company of Thorin Oakenshield and the thirteen dwarves, recognizing that the hobbit’s small size and ordinary appearance may make him a useful burglar.
In Tolkien’s mythology, Gandalf is one of the Istari, a group of supernatural emissaries sent to Middle-earth to oppose Sauron. He is also known as Mithrandir among the Elves and Men, and as Olórin in the Undying Lands. His familiar appearance is that of an old man carrying a staff.
Gandalf is not the same character as Saruman, although both are Istari. Saruman initially leads the order but is corrupted by the desire for power. Gandalf later returns in a changed form after confronting the Balrog in Moria, becoming Gandalf the White.