Eris (Greek Ἒρις, "Strife") is the goddess personifying that quality, her name being translated into Latin as Discordia. Her opposite is Concordia.
In Hesiod's Work and Days 11–-24, two different goddesses named Eris 'Strife' are distinguished:
So, after all, there was not one kind of Strife alone, but all over the earth there are two. As for the one, a man would praise her when he came to understand her; but the other is blameworthy: and they are wholly different in nature.
For one fosters evil war and battle, being cruel: her no man loves; but perforce, through the will of the deathless gods, men pay harsh Strife her honour due.
But the other is the elder daughter of dark Night (Nyx), and the son of Cronus who sits above and dwells in the aether, set her in the roots of the earth: and she is far kinder to men. She stirs up even the shiftless to toil; for a man grows eager to work when he considers his neighbour, a rich man who hastens to plough and plant and put his house in good order; and neighbour vies with is neighbour as he hurries after wealth. This Strife is wholesome for men. And potter is angry with potter, and craftsman with craftsman, and beggar is jealous of beggar, and minstrel of minstrel.
In Hesiod's Theogony (226–-232) Strife the daughter of Night is less kindly spoken of as she brings forth other personifications as her children:
But abhorred Eris ('Strife') bare painful Ponos ('Toil/Labor'), Lethe ('Forgetfulness') and Limos ('Famine') and tearful Algea (Pains/Sorrows), Hysminai ('Fightings/Combats') also, Machai ('Battles'), Phonoi ('Murders/Slaughterings'), Androctasiai ('Manslaughters'), Neikea ('Quarrels'), Pseudea ('Lies/Falsehoods'), Amphillogiai ('Disputes'), Dysnomia ('Lawlessness') and Ate ('Ruin/Folly'), all of one nature, and Horkos ('Oath') who most troubles men upon earth when anyone wilfully swears a false oath.
Strife whose wrath is relentless, she is the sister and companion of murderous Ares, she who is only a little thing at the first, but thereafter grows until she strides on the earth with her head striking heaven. She then hurled down bitterness equally between both sides as she walked through the onslaught making men's pain heavier.
Zeus sends her to rouse the Achaeans in Book 11 of the same work.
The most famous tale of Eris ('Strife') recounts her initiating the Trojan War. The goddesses Hera, Athena and Aphrodite had been invited along with the rest of Olympus to the forced wedding of Peleus and Thetis, who would become the parents of Achilles, but Eris had been snubbed because of her troublemaking inclinations.
She therefore (in a fragment from the Cypria as part of a plan hatched by Zeus and Themis) tossed into the party the Apple of Discord, a golden apple inscibed Kallisti – "For the most beautiful one", or "To the Prettiest One" – provoking the goddesses to begin quarreling about the appropriate recipient. The hapless Paris, Prince of Troy, was appointed to select the most beautiful. Greek mythological morality being what it was, each of the three goddesses immediately attempted to bribe Paris to choose her. Hera offered political power; Athena promised skill in battle; and Aphrodite tempted him with the most beautiful woman in the world: Helen, wife of Menelaus of Sparta. Paris was a red-blooded young man, and while the length of time he meditated on this problem is not recorded, he did eventually award the apple to Aphrodite.
In Nonnus' Dionysiaca, 2.356, when Typhon prepares to battle with Zeus:
Eris ('Strife') was Typhon's escort in the melée, Nike ('Victory') led Zeus to battle.
Eris has been adopted as the matron deity of the modern Discordian religion. In the process, however, she has lightened up considerably in comparison to the rather malevolent Graeco-Roman original. A quote from the Principia Discordia, the holy book of the Discordian religion, attempts to clear this up:
One day Mal-2 consulted his Pineal Gland* and asked Eris if She really created all of those terrible things. She told him that She had always liked the Old Greeks, but that they cannot be trusted with historic matters. "They were," She added, "victims of indigestion, you know." (http://www.ology.org/principia/)
The story of Eris being snubbed and indirectly starting the Trojan War is recorded in the Principia, and is referred to as the Original Snub. An added part missing from the Greek version is that after rolling the apple into the party, she left to be alone and joyously partake of a hot dog.