Each member is greeted personally by Lady Galadriel, who is lovely to behold. Her husband the Lord Celeborn is also handsome. The Lord and Lady are appraised of what the company has been doing till now and they are truly sorrowful when they hear of Gandalf's fate.
The adventurers stay for many days, resting and healing themselves as well as mourning Gandalf. One day Lady Galadriel shows Frodo and Sam her mirror, which is a basin of water from a nearby stream. When she breathes on the water, Sam and Frodo see scenes from the past and the future. When Sam looks into it, he sees his home has been dug up and his father is all alone; he wants to go home. When Frodo looks into the mirror he sees a single eye which is looking for something. The Ring around his neck gets heavier and heavier, but just as he is about to slip forward the lady makes the vision vanish.
Frodo offers his Ring to her when he realizes that she wears one of the three lesser rings, but she tells him that if she takes it se will be corrupted, as will anyone else. She refuses his offer and hopes that Frodo succeeds in his mission, though that would mean the discovery of the elves that she has managed to keep hidden from Sauron by use of her rings.
Galadriel knows what the others discussed at the council meeting: if one wants to gain something dear, one might have to sacrifice. The greater good of destroying the ring may very well mean the individual and personal sacrifices of her and her beloved elves.
Galadriel gives the company boats in order to float down the Anduin. She gives each of them a gift, in order to help them on their way. She gives Aragorn a sheath made to fit his sword and a silver broach that holds a clear green stone, the Elfstone of the house of Elendil. To Boromir, she gives a belt of gold. To Legolas she gives a bow strung with elf-hair and a quiver of arrows. To Merry and Pippin, she gives silver belts with golden clasps. To Sam she gives neither something to keep him on the road nor to defend himself; instead she gives him a box of earth from her gardens, so that when he returns to his barren and desolate home, his garden will bloom like none other. When she asks Gimli what he wants, he asks for a strand of her hair. She gives him three as well as a blessing that his hands will flow with gold, though it will have no dominion over him. To Frodo she bequeaths a small crystal Phial in which is caught the light of Earendil's star, amid the waters of a fountain. It will be a light for him in dark places and make the night brighter.
The company then leaves and goes on their way. They have chosen a difficult, but a valiant path.
The path he men have chosen is clearly the path of good, as opposed to evil, which is the essential conflict in the novel. Lady Galadriel's psychic powers and Sam's vision of the Shire being laid waste by some kind of industry are perhaps social comments pointing towards the change that was taking place during World War I (in which Tolkien served), or during World War II (during which The Lord of the Rings was written).
The journey by boat is uneventful for a few days. They pass barren lands laid waste by Sauron and come across no living things except black swans flying overhead. The company decides to follow Aragorn along the path he recommends. Boromir disagrees, wanting to return to his home with the Ring, because of the dream he had. Aragorn and Legolas go on ahead to find a safe route; they return to tell the company that they must leave the river and go by road for a while.
Not much happens here. The most significant thing is the foreshadowing of the eventual conflict between Boromir and Frodo. Boromir wants to take the Ring back to his people. Clearly, this will not fit in with Frodo's aim. The tragic consequences of this disagreement will affect everyone.
That night the company rests on the right bank at the foot of Amonthen. The next day the burden of choice is laid on Frodo's shoulders. He must decide whether to return with Boromir to Gondor and defeat Sauron, or proceed with the plan to destroy the Ring.
Frodo takes a walk. Boromir follows him and tries to persuade him to return with the ring to Gondor. Frodo refuses and says that if he does not take the difficult path to Mount Doom and destroy the Ring, every good battle will ultimately be lost.
In desperation, Boromir tries to take the Ring. Frodo slips it on and evades Boromir, who comes to his senses and realizes what he has done.
Frodo is aware that the others must be looking for him. He puts the Ring on again and goes towards the foot of the hill, realizing that he must proceed alone, to avoid further complications. The company learns from Boromir part of what has happened and they pair off to go and look for him. On a hunch Sam goes to the river where he sees an empty boat floating. He jumps towards it but misses and falls into the water. Frodo takes off his Ring and helps Sam ashore. After much arguing, Frodo agrees that Sam should accompany him and the two of them set out toward the Land of Shadow.
The unexpected complication of Boromir's desperation has made Frodo realize the enormity of his responsibility. He decides to travel on alone rather than see any of his other companions overcome by desperation or the evil spell of Sauron.