Knowledge of Angels traces the stories of two outsiders, who change the medieval Mediterranean island of Grandinsula forever. The outsiders are discovered at about the same time. Their fates are intertwined, but they never meet. The novel is set in the time of the religious intolerance of the Spanish Inquisition, and the island is deeply affected by an Inquisitor, who comes to the island to flush out heretics.

Shepherds and local ice dealers discover Amara, a child who has been raised by wolves, high in the Grandinsulan mountains. She is wild and savage, and the men almost kill her before Jaime, a shepherd, realizes that she is a child. Jaime feels responsible for Amara, and eventually takes her to Severo, the island's Prince and Cardinal. Jaime is gravely concerned that the child is not baptized.

Meanwhile, a beautiful swimmer is found off the shore of a small fishing village. Miguel and Lazaro, two fishermen, rescue Palinor and bring him back to health. Palinor tells them he is from a far off island called Aclar, and he later reveals that he is an engineer, architect, and King of Aclar who fell off one of his ships while trying to free the rudder. He started swimming, and he ended up on Grandinsula. Everyone who encounters Palinor notices his regal manner and respectful ways.

Palinor tells the local prefect that he does not believe in God when asked what his religion is for a standard form. The prefect is taken aback, as everyone in Grandinsula is some form of Christian. Palinor is jailed for his heresy, as is law on the island, and eventually Palinor appeals to Severo. Severo takes an immediate liking to Palinor, and instead of having him burned according to law or sending him back to Aclar, Severo calls in Beneditx, the island's leading scholar to convince Palinor that God exists.

Severo also has a plan for Amara, who he believes can prove that the knowledge of God is not innate. He sends Amara to Sant Clara, where a young novice, Josefa, is charged with teaching the wolf-child to talk, walk upright, and act civilized. Under no circumstances are the nuns to mention God to Amara. Once Amara can talk, Severo wants to question her about God, and when she was with the wolves.

Palinor never accepts any of Beneditx's proofs of God, and eventually Beneditx is the one who loses his faith. In a fit of anger, Severo turns Palinor over to Fra Murta, an Inquisitor. Palinor recants once under extreme torture, but later says he didn't mean it. Severo is unable to save Palinor, and the atheist is burned alive at a pyre outside the island's capital.

When Severo and Fra Murta first question Amara, who has learned to speak, she denies any knowledge of God. Fra Murta believes she simply did not understand the questions, so they return later. This time, Josefa coaches Amara, and she replies that she did sense God's presence, when she was with the wolves. In return, Amara gets her freedom from the convent, which she has been longing for, but her response does not help Palinor.

Jaime gets Amara a job taking care of the nevados' ice hut. As soon as Jaime leaves her there, however, Amara begins climbing the mountain. She climbs higher and higher, turning once to glimpse a large armada heading toward Grandinsula, which is a fleet from Aclar seeking revenge for Palinor's death. Amara stays above the fray, continuing to climb the highest summit.