Eve is derived from the Hebrew word which means living, or life giver, and by extension, mother. While all subsequent humans have Eve as an ancestor, she is unique in that although all people after her were physically created from women, Eve herself was created from a man.
The Creation Of Eve
"Then The Lord God said, "It is not good that the man should be alone; I will make him a helper fit for him." (Genesis 2:18 RSV)
"So The Lord God caused a deep sleep to fall upon the man, and while he slept took one of his ribs and closed up its place with flesh; and the rib which The Lord God had taken from the man he made into a woman and brought her to the man. Then the man said, "This at last is bone of my bones and flesh of my flesh; she shall be called Woman, because she was taken out of Man." (Genesis 2:21-23 RSV) (see The Seven Days Of Creation and The Creation Of Adam And Eve)
"Now the serpent was more subtle than any other wild creature that The Lord God had made. He said to the woman, "Did God say, 'You shall not eat of any tree of the garden'?" (see That Old Serpent and Did God Create The Devil?)
"And the woman said to the serpent, "We may eat of the fruit of the trees of the garden; but God said, 'You shall not eat of the fruit of the tree which is in the midst of the garden, neither shall you touch it, lest you die.'"
"But the serpent said to the woman, "You will not die. For God knows that when you eat of it your eyes will be opened, and you will be like God, knowing good and evil." (see Satan's Language)
"So when the woman saw that the tree was good for food, and that it was a delight to the eyes, and that the tree was to be desired to make one wise, she took of its fruit and ate; and she also gave some to her husband, and he ate. Then the eyes of both were opened, and they knew that they were naked; and they sewed Fig leaves together and made themselves aprons." (Genesis 3:1-7 RSV)
Banished From The Garden Of Eden
"Then The Lord God said to the woman, "What is this that you have done?" The woman said, "The serpent beguiled me, and I ate." (Genesis 3:13 RSV)
"And The Lord God made for Adam and for his wife garments of skins, and clothed them. Then The Lord God said, "Behold, the man has become like one of us, knowing good and evil; and now, lest he put forth his hand and take also of the tree of life, and eat, and live for ever" - therefore The Lord God sent him forth from the garden of Eden, to till the ground from which he was taken. He drove out the man; and at the east of the garden of Eden he placed the cherubim, and a flaming sword which turned every way, to guard the way to the tree of life." (Genesis 3:21-24 RSV)
Fact Finder: Did Adam and Eve begin having children before, or after, they left the Garden of Eden?
Genesis 3:23, 4:1-2
See Cain and Abel