Princess Andromeda

The "Princess Andromeda" is a cruise ship captained by Luke and is the primary living space for Kronos' Army. It contains Kronos' sarcophagus, and can travel very quickly faster then any mortal ship, possibly assisted by magic or a titan.

The Sea of Monsters
In The Sea of Monsters, Luke is in control of the ship. Hermes sends Percy onto it so he can talk to Luke which Hermes lives Percy to get to himself. The ship has many mortals on it, but they are all under some sort of trance that prevents them from seeing the real thing there or noticing the disemboweling practice. A few days later, Luke takes Percy on board to take the fleece. The Party Ponies attack putting Kronos' army in confusion when Luke and Percy are dueling to the death.

The Titan's Curse
In The Titan's Curse, the Princess Andromeda is only mentioned twice, when Tyson tells Percy it is near the Panama Canal, and when it is at Mount Tamalpais unloading the titans army.

The Last Olympian
In The Last Olympian, Percy and Beckendorf board the ship, with the intention of destroying it with Greek fire. They notice that it is filled with Telekhines and other members of the Titan army, and that the once plush carpets had been ruined by slime. There are no more mortals on the ship which Percy thinks didn't get to leave with their bingo winnings. They manage to destroy the ship by blowing it up, but Beckendorf dies by sacrificing his life.

Trivia

 * The ship is name after the famous princess Andromeda who was nearly fed to Cetus before Perseus, Percy's namesake slew it with Medusa's head. As a result a figurehead of a woman is chained to the bow of the ship as she was.