History
In Greek mythology, Ἀχιλλεύς, grandson of Aeacus  Akhilleus Aiákidês, also transliterated as Achilleus, Akhilles, or Akhilleus) was the greatest and the central character of Homer's Iliad.

Achilles was the son of Peleus, king of the Myrmidons in Phthia (southeast Thessaly), and the sea nymph Thetis. Zeus and Poseidon had forced her for her hand until Prometheus the fire bringer revealed she would bear a son greater than his father, whence they wisely chose to give her to someone else. According to legend, Thetis had tried to make Achilles invincible by dipping him in the river Styx, but forgot to wet the heel she held him by, leaving him vulnerable so he could be killed by a blow to that heel.

During the Trojan War
Achilles is one of the only two people described as "god-like" in the Iliad. This does not just refer to his supreme fighting ability, but also to his attitude. He shows a complete and total devotion to the excellence of his craft and, like a god, has almost no regard for life. Not his own — clearly he does not mind a swift death, so long as it is glorious (kleos) — and not really of others. His anger is absolute. The humanization of Achilles by the events of the war is the main theme of the Iliad.

Achilles' charioteer's name was Automedon.

Troilus
According to Dares Phrygius' Account of the Destruction of Troy[[1]], while this youngest son of Priam and Hecuba (some say that it was Apollo who fathered Troilus on Hecuba) was watering his horses at the Lion Fountain outside the walls of Troy, Achilles saw him and fell in love with his beauty (whose "loveliness of form" was described by Ibycus as being like "gold thrice refined"). The youth rejected his advances and took refuge inside the temple of Apollo Timbraeus. Achilles pursued him into the sanctuary and decapitated him on the god's own altar. (Tzetzes, scholiast on Lycophron). At the time Troilus was said to be a year short of his twentieth birthday, and the legend goes that if Troilus had reached his twentieth year, Troy would have been invincible. (First Vatican Mythographer)

Agamemnon and the death of Patroclus
Achilles took twenty-three towns outside Troy, including Lyrnessos, where he captured Briseis to keep as a concubine. Meanwhile, Agamemnon took a woman named Chryseis and taunted her father, Chryses, a priest of Apollo, when he attempted to buy her back. Apollo sent a plague through the Greek armies and Agamemnon was forced to give Chryseis back to her father; however he took Briseis away from Achilles as compensation for his loss. This action sparked the central plot of the Iliad: Achilles becomes enraged and refuses to fight for the Greeks any further. The war goes badly, through the influence of Zeus, and the Greeks offer handsome reparations to their greatest warrior. Achilles is visited by Odysseus, Ajax, and Phoenix who attempt to persuade him to return to battle, but Achilles still refuses to fight. Once the Greeks are pushed back to the ships, which are just starting to be set on fire by Hector, he agrees to allow Patroclus to fight in his place, wearing his armor. The next day Patroclus is killed and stripped of the armor by the Trojan hero Hector, who mistakes him for Achilles. Achilles is overwhelmed with grief for his friend (or homosexual lover as interpreted by the majority of ancient Greeks), and the rage he once harbored toward Agamemnon begins shifting to Hector. Thetis, his mother, rises from the sea floor and berates him for excessive grief, reminding him it is a fine thing to sleep with women too. She obtains magnificent new armor for him from Hephaestus, and he returns to the fighting, killing Hector. He desecrates the body, dragging it behind his chariot before the walls of Troy three times, and refuses to allow it to receive funeral rites. When Priam, the king of Troy and Hector's father, comes secretly into the Greek camp to plead for the body, Achilles finally relents; in one of the most moving scenes of the Iliad, he receives Priam graciously and allows him to take the body away.

The greatness of Achilles lies in not just being the greatest Greek fighter ever, but in knowing the choice provided to him by Destiny. His mother Thetis had prophesied to him that if he pulled out of the Trojan War, he would enjoy a long and a happy life. If Achilles fought, however, he would die before the walls of Troy but assure an everlasting glory, surpassing that of all other heroes. He had made the choice, and coming face to face with it showed his greatness.

Xanthus
During the Trojan War, Xanthus, a magical horse, was rebuked by Achilles for allowing Patroclus to be killed. Xanthus responded by saying that a god had killed Patroclus and a god would soon kill Achilles too.

Memnon, Cycnus, Penthesilea, and the death of Achilles
Shortly after the death of Hector, Achilles defeated Memnon of Ethiopia, Cycnus of Colonae and the Amazonian warrior Penthesilia (with whom Achilles also had an affair in some versions). As predicted by Hector with his dying breath, Achilles was thereafter killed by Paris — either by an arrow to the heel, or in an older version by a knife to the back while visiting Polyxena, a princess of Troy. Both versions conspicuously deny the killer any sort of valor, and Achilles remains undefeated on the battlefield. His bones are mingled with those of Patroclus, and funeral games are held. Like Ajax, he is represented (although not by Homer) as living after his death in the island of Leuke at the mouth of the Danube.

The Fate of Achilles' armor
Achilles' armor was the object of a feud between Odysseus and Ajax the Greater. They competed for it and Odysseus won. Ajax went mad with grief and vowed to kill his comrades; he started killing cattle (thinking they were Greek soldiers), and then himself.