The elf-king who rules the Woodland Realm in J.R.R. Tolkien’s The Hobbit is Thranduil.
Thranduil is the Elvenking of the Woodland Realm, also called the realm of the Silvan Elves in northern Mirkwood. In The Hobbit, his soldiers capture Thorin Oakenshield and the other dwarves after the company escapes from the giant spiders. The king keeps them in his underground halls until Bilbo helps them flee in barrels.
Thranduil is Legolas’s father. Tolkien does not name him in The Hobbit itself; the name appears in later writings and related chronology. This is one reason readers sometimes identify him only as “the Elvenking” when discussing the novel.
His kingdom is not Rivendell, which is ruled by Elrond, nor Lothlórien, associated with Galadriel and Celeborn. Thranduil’s Woodland Realm is in Mirkwood, a forest transformed by the influence of the Necromancer, later revealed as Sauron.