Medusa

From Camp Halfblood

Medusa is a Monster that appears in The Lightning Thief. Posing as a human, Medusa lures people into her 'mannequin' shop and then turn them into statues themselves by looking at them. At one point, Percy, Annabeth, and Grover are lured into the shop during their Quest. Medusa feins kindness, and then attempts to turn them into statues. After a long struggle, Percy defeats Medusa. Her severed head is later used by Percy for several purposes.

It also seems that Medusa was exceptionally kind to Percy, and wanted him to stay with her forever by becoming a statue because, according to Annabeth, she and Poseidon had a thing in the past. Since Percy was Poseidon's son, she wanted him. That thing also led to part of the (and probably the most important) reason Athena resents Poseidon; he desecrated her temple with Medusa by kissing in it. Medusa wanted to stone Annabeth as revenge on Athena for turning her into a monster.