She was the Goddess of All Things, and desired to make order out of the Chaos. By coupling with a huge and powerful snake, Ophion, or as some legends say, coupling with the North Wind, she gave birth to Eros, god of Love, also known as Protagonus, the "firstborn".
Eurynome separated the sky from the sea by dancing on the waves of Oceanus. In this manner, she created great lands upon which she might wander, a veritable universe, populating it with exotic creatures such as Nymphs, Furies, and Charites as well as with countless beasts and monsters.
Also born out of Chaos were Gaia, called Earth, or Mother Earth, and Uranus, the embodiment of the Sky and the Heavens, as well as Tartarus, god of the sunless and terrible region beneath Gaia, the Earth.
In what has become one of the recurrent themes of Greek Mythology, Gaia and Uranus warned Cronus that a son of his would one day overpower him. Cronus therefore swallowed his numerous children by his wife Rhea, to keep that forecast from taking place.
This angered Gaia greatly, so when the youngest son, Zeus, was born, Gaia took a stone, wrapped it in swaddling clothes and offered it to Cronus to swallow. This satisfied Cronus, and Gaia was able to spirit the baby Zeus away to be raised in Crete, far from his grasping father.
In due course, Zeus grew up, came homeward, and got into immediate conflict with the tyrant Cronus, who did not know that this newcomer was his own son. Zeus needed his brothers and sisters help in slaying the tyrant, and Metis, Zeus's first wife, found a way of administering an emetic to Cronus, who then threw up his five previous children, who were Hestia, Demeter, Hera, Hades, and Poseidon. Together they went to battle against their father. The results were that all of his children, led by Zeus, vanquished Cronus forever into Tartarus' domain, the Dark World under the Earth.
Thus, Zeus triumphed over not only his father, and his father's family of Giants, he triumphed over his brothers and sisters as well, dividing up the universe as he fancied, in short, bringing order out of Chaos.
He made himself Supreme God over all, creating a great and beautiful place for his favored gods to live, on Mount Olympus, in Thessaly. All the others were left to fend for themselves in lands below Mount Olympus.
Zeus made himself God of the Sky and all its phenomena, including the clouds as well as the thunderbolts. Hestia became goddess of the Hearth. To his brother Poseidon, he gave the rule of the Sea. Demeter became a goddess of Fertility, Hera (before she married Zeus and became a jealous wife), was goddess of Marriage and Childbirth, while Hades, one of his other brothers, was made god of the Underworld.
Zeus did indeed bring order out of Chaos, but one of his failings was that he did not look kindly upon the people, those creatures that populated the lands over which he reigned. Many were not beautiful, and Zeus had contempt for anyone who was not beautiful. And of course they were not immortal, as the Olympian gods were, and they complained about the lack of good food and the everlasting cold nights. Zeus ignored their complaints, while he and the other gods feasted endlessly on steaming hot game from the surrounding forests, and had great crackling fires in every room of their palaces where they lived in the cold winter.
Enter Prometheus, one of the Titans not vanquished in the war between Zeus and the giants. It is said in many myths that Prometheus had created d a race of people from clay, or that he had combined specks of every living creature, molded them together, and produced a new race, The Common Man. At the very least he was their champion before Zeus.
Fire for cooking and heating was reserved only for the gods to enjoy. Prometheus stole some of the sparks of a glowing fire from the Olympians, so that the people below Olympus could have fire for cooking and warmth in the winter, thus greatly improving their lot in life.
Zeus was furious at this insult to his absolute power, and had Prometheus bound and chained to a mountain, sending an eagle to attack him daily.
Adding insult to injury, Zeus had his fellow Olympian, Hephaestus, fashion a wicked but beautiful creature to torment Prometheus. It was a woman, whom they named Pandora, which means "all gifts". She was given a precious and beautiful box, which she was told not to open, but curiosity got the better of her, and out flew "all the evils that plague men." The only "gift" that stayed in the box was "Hope".
So, from "far-ruling" Eurynome to the creation of the Common Man, Greek creation myths are inextricably filled with difficulties, though often ameliorated by the gift of Hope. A myriad of other myths tell of the joys and adventures of great heroes and heroines, other gods and goddesses, as well as fantastic creatures from all parts of ancient Greece.
Every myth, Greek or otherwise, that has ever been told or written, varies in the telling. The basic themes are repeated in many of them, but details, even story lines will differ considerably, from village to village, eon to eon.
When one understands that the myths have been told for many centuries before being written down, which first occurred about 800 BCE, one can relish the differences in the tellings and enjoy the Greek's brilliant and artful imagination throughout the ages.