"The Aleph" is a short story, which superficially is about the relationship of the narrator, Borges, to the cousin of a woman Borges once loved. The woman, Beatriz Viterbo, dies in 1929, but Borges continues to visit her home every April 30th, which is the anniversary of her birthday. Still living at Beatriz' home are her father and her cousin, Carlos Argentino Daneri. Borges eventually forms an uneasy friendship with Carlos, who introduces Borges to a magical sphere, which Daneri names an Aleph.

The story opens with an epigraph consisting of two quotes: one from Shakespeare's play, Hamlet, and the other from a work titled, Leviathan, by Thomas Hobbs. The first quote, "O, God, I could be bounded in a nutshell and count myself a King of infinite space," is very clearly a reference to an Aleph, which Carlos discovers at stair nineteen in his basement...