Bilbo regains consciousness and, finding himself alone, tries to crawl through the tunnel. He finds a ring, which he absentmindedly pockets. He wishes he were back in his comfortable home, eating. As a hobbit, he can orient himself quite well underground, and he continues to descend the tunnel until he comes to a lake that he cannot cross, not knowing how to swim.
Bilbo is spotted by old Gollum, who lives alone on an island in the lake, which he navigates in a small boat. Gollum is a small, slimy, dark creature with pale eyes, named for the sound he makes as he swallows; he preys upon Goblins and fish. Because he lives alone, Gollum is in the habit of speaking to himself in a kind of hissing baby-talk, calling himself "my precious." Trying to assess Bilbo, he engages him in a game of riddles, at which Bilbo proves his equal.
Gollum decides to get the better of Bilbo by using his birthday present, a ring. When he wears it, he is invisible and can more easily snag his prey. He goes to the hiding place where he keeps the ring, but it is gone. Gollum correctly surmises that Bilbo has it and confronts him, asking what is in his pocket. Bilbo, who does not understand the power of the ring, slips it on his finger as Gollum runs to attack him. Bilbo becomes invisible, and Gollum cannot find him to attack.
Gollum is afraid that without the invisibility of the ring, he will be captured by the Goblins. He panics and runs to escape the cave. Bilbo, who is still invisible, follows him, thereby discovering the way out. Gollum, who can smell Bilbo, blocks his way. Bilbo thinks of killing Gollum, but decides it would not be fair, because Bilbo is invisible and Gollum is unarmed. Bilbo escapes by an extraordinary leap over Gollum's head and through the passageway, but he runs into the Goblins. As they rush at him, he slips the ring on, becoming invisible, and narrowly escapes to the outside where it is light and the Goblins cannot follow.
In this chapter, Bilbo finds himself alone when confronting danger; he is without the company of the dwarves or the direction of Gandalf. He relies effectively on his own ingenuity and resourcefulness to outwit both Gollum and the Goblins. In this and in taking the final leap over Gollum and out of the cave, Bilbo demonstrates a bravery that he did not know he possessed. He also demonstrates a sense of ethics when he decides not to kill Gollum because of his unfair advantages of invisibility and a weapon. Thus you see Bilbo developing beyond his hobbit mildness into someone who can survive danger by using good judgment and taking appropriate risks.
The depiction of Gollum is a masterpiece of symbolic characterization. He lives alone, on an island, and is so inexperienced in any kind of social interaction that he can speak only to himself, which he does constantly; additionally, his lack of development is indicated by the babyish nature of his language. Bilbo encounters Gollum when he is himself alone, trying to rejoin the dwarves. You thus see Bilbo in a kind of symbolic confrontation with a self-absorbed, immature individual, who may faintly resemble the hobbit-like disinclination to venture out into the world. Bilbo's leap over Gollum to escape the cave emphatically represents a leap he takes in his own personal development.
It is interesting to note that Tolkien heavily revised this chapter some years after the first edition of The Hobbit, when he was working on The Lord of the Rings trilogy, in order to provide a history for the ring that is so important to those books.