Styx

The River Styx is a river located in the Underworld. According to Percy the river is very polluted, being filled with pretty much anything you could imagine, broken toys, ripped up diplomas etc. The river is filled with broken dreams, lost when the person died. The diploma symbolizing that a student with dreams of going to college died before they could finish.

The River is also part of a powerful promise that can be made between people and breaking an oath on the Styx is extremely unwise for anyone. Gods who break oaths on the Styx apprently "get off lightly" on the account of being Immortal such as when Zeus broke the oath between himself and his brothers of having no more demigod children. It is unkown what would happen if a lesser entity were to break an oath on the Styx but it is considered unpleasant. The River Styx is also where Stygian iron is cooled which makes indestructable.

Achilles' Curse
Anyone who bathes in the River Styx will be gifted with the strength, power, speed, and near invincibility of Achilles. The only spot where one who has bathed in the River Styx is vulnerable is in their 'Achilles Heel', a spot of the bather's choosing which will keep them grounded to the real world and their mortal life after they bathe in the river. If the person doesn't focus on that point while bathing in the river they will be destroyed, washed away in the current. Achilles' ghost appears to anyone who wishes to receive the curse, warning them not to. The ghost claims it will affect them highly but shows few signs in Percy.

People known to have bathed in the River Styx
There have only been three people to have bathed in the river and lived:
 * Achilles - His mother dipped him into the River by his heel. Therefore, his heel is vulnerable.
 * Luke Castellan - Luke having done so to become invincible so his body could hold Kronos' spirit. His Achilles spot is under his left armpit. He envisioned himself and Thalia first meeting and starting a romantic relationship and giving his knife to Annabeth Chase.
 * Percy Jackson - Percy having done so to gain the power needed to beat Luke. His Achilles is the small of his back. He envisioned being pulled from the Canoe lake by Annabeth Chase, the girl he loves, who later becomes his girlfriend.