Seed of the woman
The seed of the woman or offspring of the woman is a concept, drawn from Genesis 3:15, which is viewed differently in Judaism and Christianity. In Christianity it is often given a Messianic interpretation.
ואיבה אשית בינך ובין האשה ובין זרעך ובין זרעה הוא ישופך ראש ואתה תשופנו עקב׃
- wə·’ê·ḇāh ’ā·šîṯ, bê·nə·ḵā ū·ḇên hā·’iš·šāh, ū·ḇên zar·‘ă·ḵā ū·ḇên zar·‘āh; hū yə·šū·p̄ə·ḵā rōš, wə·’at·tāh tə·šū·p̄en·nū ā·qêḇ.
- ESV translation:
I will put enmity between you and the woman,
and between your offspring and her offspring;
he shall bruise your head,
and you shall bruise his heel.”
In rabbinical Judaism the contrasting groups of "seed of the woman" and "seed of the serpent" are generally taken as plural, and the promise "he will bruise your head" applied to Adam / mankind bruising the serpent's head.
Although a possible Jewish messianic interpretation of Genesis 3:15 in some schools of Judaism during the Second Temple Period has been suggested by some Christian scholars, no evidence of such an interpretation has yet come to light.
Identification of the "seed of the woman" with Christ goes back at least as far as Irenaeus and the phrase "Seed of the woman" is sometimes counted as one of the titles of Jesus in the Bible. A tradition found in some old eastern Christian sources (including the Kitab al-Magall and the Cave of Treasures) holds that the serpent's head was crushed at Golgotha, described as a skull-shaped hill at the centre of the Earth, where Shem and Melchizedek had placed the body of Adam. More commonly, as in Victorian homilies, "It was on Golgotha that the old serpent gave the Saviour the deadly bite in his heel, which went quite through his foot, fastening it to the cross with iron nails."
Luther, in his commentary on Genesis (Luther's Works, vol. 1, pp. 192-193, American Edition), identifies the "seed of the woman" as the coming Messiah, Jesus, and not Mary: "When we are given instruction in this passage concerning the enmity between the serpent and woman--such an enmity that the Seed of the woman will crush the serpent with all his powers--this is a revelation of the depths of God's goodness...[who] clearly declares that the male Seed of the woman would prostrate this enemy."
In a derived sense, Luther in his Lectures on Romans identifies the seed of the woman with the word of God in the church. 
Some Catholics may understand the promise of a "seed" to Eve as primarily relating to Mary herself not Christ. The English Douay–Rheims Bible 1609 onwards has "she (Mary) shall crush thy head, and thou shalt lie in wait for her heel." The reading was supported in the Bull Ineffabilis Deus of December 1854, and is defended in the Catholic Encyclopedia (1912), where Anthony Maas acknowledges that the Douay–Rheims does not follow the Hebrew.
Maas also writes: "One may be tempted to understand the seed of the woman in a similar collective sense, embracing all who are born of God. But seed not only may denote a particular person, but has such a meaning usually, if the context allows it. St. Paul (Galatians 3:16) gives this explanation of the word "seed" as it occurs in the patriarchal promises: "To Abraham were the promises made and to his seed. He saith not, and to his seeds, as of many; but as of one, and to his seed, which is Christ."
The Catholic Encyclopedia also states,
The translation "she" of the Vulgate is interpretative; it originated after the fourth century, and cannot be defended critically. The conqueror from the seed of the woman, who should crush the serpent's head, is Christ; the woman at enmity with the serpent is Mary.  The New Jerusalem Bible retains "she shall crush thy head, and thou shalt lie in wait for her heel".
The Anglican/Roman Catholic International Commission explains the controversy:
“The Hebrew text of Genesis 3:15 speaks about enmity between the serpent and the woman, and between the offspring of both. The personal pronoun (hu’) in the words addressed to the serpent, “He will strike at your head”, is masculine. In the Greek translation used by the early Church (LXX), however, the personal pronoun autos (he) cannot refer to the offspring … but must refer to a masculine individual who could then be the Messiah, born of a woman. The Vulgate (mis)translates the clause as ipsa … This feminine pronoun supports a reading of this passage as referring to Mary which has become traditional in the Latin Church.
The revised Latin version (Nova Vulgata) authorized by the Vatican, corrected the error and changed it from ipsa to ipsum in the Latin. 
The notes in the Catholic New American Bible, explains this verse,
They will strike…at their heel: the antecedent for “they” and “their” is the collective noun “offspring,” i.e., all the descendants of the woman. Christian tradition has seen in this passage, however, more than unending hostility between snakes and human beings. The snake was identified with the devil (Wis 2:24; Jn 8:44; Rev 12:9; 20:2), whose eventual defeat seemed implied in the verse. Because “the Son of God was revealed to destroy the works of the devil” (1 Jn 3:8), the passage was understood as the first promise of a redeemer for fallen humankind, the protoevangelium. Irenaeus of Lyons (ca. A.D. 130–200), in his Against Heresies 5.21.1, followed by several other Fathers of the Church, interpreted the verse as referring to Christ, and cited Gal 3:19 and 4:4 to support the reference
- Jacob, Neusner (1984). Our Sages, God, and Israel. Chappaqua: Rossel Books. p. 165. ISBN 0940646188. "Man became frightened, saying: This is the one concerning whom it is written: He will bruise your head, and you shall bruise his heel, Genesis 3:15. Perhaps this one has come to bite me."
- Eisenmenger, Johann Andreas (2006). J P Stehelin and Michael A Hoffman II, ed. The Traditions of the Jews (1st ed.). Coeur d'Alene: Independent History and Research. ISBN 0970378440.
- Patai, Raphael (1986). The Messiah Texts. Detroit: Wayne State University Press. ISBN 0814318509.
- Mcdowell, Josh (2007). Nueva Evidencia Que Demanda un Veredicto [English: New Evidence that Demands a Verdict] (in Spanish). Casa Bautista of Pubns. p. 334. ISBN 0311050484. "Aquí Dios promete que la simiente de la mujer aplastaría la cabeza de la serpiente. Claus Westermann, un experto en el Antiguo Testamento, afirma: "Desde el tiempo de Ireneo, la tradición cristiana ha entendido este pasaje como una profecía acerca de Cristo (y María)"
- Armour, Michael C (2002). A Newcomer's Guide to the Bible. Joplin: College Press Publishing Company. p. 43. ISBN 0899009018. "To remove those barriers, God made a special promise to Eve. Before He sent her from the garden, He promised that one of her descendants would eventually crush Satan's head, receiving a painful bruise in the process (Genesis 3:15)."
- Budge, Ernest Aldfred Wallis (2010). The Book of the Cave of Treasures. Whitefish: Kessinger Publishing, LLC. p. 127. ISBN 1169774628. "And it was called "Gaghulta," because it was round Pike the head], and "Resiphta" (ie a trodden-down thing), because the head of the accursed serpent, that is to say, Satan, was crushed there, and "Gefifta" (Gabbatha), because all the nations were to be gathered to it." Kitab al-Magall: "The place was called Gumgumah, "of a skull", because in it was placed the skull of the Father of mankind, and Gulgulah, because it was conspicuous in the earth, and was despised by its sons, for in it was the head of the hateful Dragon which seduced Adam."
- Arnot, William (2010). The Family Treasury. Nabu Press. ISBN 1147041121.
- Luther, Martin (1958). Luther's Works, American Edition. St. Louis, MO: Concordia Publishing House. pp. 192–193.
- Luther, Martin; Pauck, translated by Wilhelm (1961). Luther: Lectures on Romans (Ichthus ed.). Louisville: Westminster John Knox Press. p. 183. ISBN 0664241514. "The seed of the devil is in it; hence, the Lord says to the serpent in Gen. 3:15: "I will put enmity between your seed and her seed." The seed of the woman is the word of God in the church,"
- Maas, Anthony (2009). "The Blessed Virgin Mary". Catholic Encyclopedia. Retrieved 3 May 2012.
- The Catholic Encyclopedia, Immaculate Conception
- Anglican/Roman Catholic International Commission, Donald Bolen, Gregory Cameron, Mary: grace and hope in Christ : the Seattle statement of the Anglican-Roman Catholic International Commission ; the text with commentaries and study guide, [Continuum International Publishing Group, 2006], p. 33 footnote 4