The wizard character who guides Bilbo Baggins in J.R.R. Tolkien’s stories is Gandalf.
Gandalf appears in The Hobbit as the organiser of the Dwarves’ expedition to reclaim the Lonely Mountain. He selects Bilbo as the company’s burglar and helps set the quest in motion. In The Lord of the Rings, Gandalf becomes one of the principal leaders opposing Sauron and helps Frodo understand the danger of the Ring.
The character has different appearances and names across Tolkien’s legendarium. In Middle-earth, he is known as Gandalf the Grey and later Gandalf the White. Tolkien also gives him names such as Mithrandir among the Elves and Men of Gondor, and Tharkûn among the Dwarves.
Gandalf is not one of the Valar, despite his extraordinary power. He is a Maia, a spirit sent to Middle-earth in the guise of an old man. Saruman and Radagast are fellow Istari, but neither is Bilbo’s guide.