The librarian describes the universe of the Library. He speculates that its hexagons extend into infinity.
In his younger days, the librarian traveled in search of a book.
Now the librarian is an old man, and his sight is failing him. He's preparing to die a few leagues from where he was born.
When he dies, the narrator believes that someone will throw his body over the railing into the ventilation shaft, and that it will fall for eternity.
The librarian states it as a fact: the Library is endless.
Before he gives away the big secret to the Library, the narrator says he wants to tell us a few more basic facts.
First of all, the narrator says that the Library is clearly eternal. As an example, he contrasts the neat print of the Library's books with his own feeble handwriting.
Secondly, the librarian observes that there are 25 written symbols. He recounts the few times he or his father has seen a book that seemed to make some sort of sense, but, for the most part, he says, books are filled with gibberish.
The librarian begins to give us a history of thought in the Library. The biggest revelation, he says, came when people found out that the Library is "total." In other words, it contains every possible text ever written.
In his account of the history of the Library, the narrator has some personal encounters with some of the actors and objects. For example:
The narrator reports that he has personally seen two "Vindications" – books about individuals in the Library.
He has also seen the "inquisitors" – officials who patrol the Library, searching for meaningful books.
As a child, the narrator says he encountered members of a "blasphemous" sect who attempted to derive their own books of meaning by casting dice.
The narrator downplays the horror inspired by the destructive rage of the Purifiers, a group that tried to eliminate all worthless books. As the narrator explains, they hardly made a dent in the quantity of books in the Library, and there are plenty of books nearly identical to the ones they destroyed.
The narrator admits that he has spent years of research trying to track down a person who might have read the "total book" – a book that would decipher all other books in the Library. He offers a prayer that such a person exists and that he (yeah, probably he) has been able to comprehend the Library's mysteries.
The librarian denies that the Library is full of "non-sense," and argues that every piece of writing in the Library means something, even though we might not be able to understand it. And for that matter, we might not really understand the things we think we understand.
The narrator says that, these days, he writes in order to distract himself from the sorry state of humanity. People around him have been dropping like flies, and he figures the human race is on the verge of extinction.
As a parting thought, the narrator explains how he has reconciled the idea of an infinite Library with the knowledge that it contains a finite number of books. The Library must be periodic, he reasons – in other words, it must repeat himself. That repetition would necessarily create a kind of Order to the universe, which comforts him.