Character Analysis
Though we never actually see Kronos, he definitely has a presence in Percy's story. He talks to Percy through Percy's dreams, luring Percy down to the Underworld. Percy believes that Kronos, who is a Titan and the father/grandfather of the Olympians, is healing and is planning to overthrow the Olympians, but when he conveys this belief to Zeus, Zeus doesn't want to hear it and dismisses the idea. Luke confirms Percy's suspicion at the end of the story.
Poseidon gives a good history of Kronos:
In the First War, Percy, Zeus cut our father into a thousand pieces, just as Kronos had done to his own father, Ouranos. Zeus cast Kronos's remains into the darkest pit of Tartarus. The Titan army was scattered, their mountain fortress on Etna destroyed, their mountainous allies driven to the farthest corners of the earth. And yet, Titans cannot die, any more than we gods can. Whatever is left of Kronos is still alive in some hideous way, still conscious in his eternal pain, still hungering for power. […] From time to time over the eons, Kronos has stirred. He enters men's nightmares and breathes evil thoughts. He wakens restless monsters from the depths. But to suggest he could rise from the pit is another thing. (21.85-87)