Gen 3:1-15
1 Now the serpent was more subtil than any beast of the field which the LORD God had made. And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the garden?

The "serpent" is one of Satan's names.
Satan is very subtle and quite proficient in the use of subterfuge.

subtle \set-el\ adj subtler \set-el-er\; subtlest \set-el-est\ 1 : hardly noticeable <~ differences> 2 : shrewd, perceptive 3 : clever, sly subtlety \-te\ n subtly \set-el-e\ adv
(C) 1995 Zane Publishing, Inc. The Merriam-Webster Dictionary (C) 1994 by Merriam-Webster, Incorporated

subterfuge \seb-ter-fyuj\ n : a trick or device used in order to conceal, escape, or evade syn fraud, deception, trickery 
(C) 1995 Zane Publishing, Inc. The Merriam-Webster Dictionary (C) 1994 by Merriam-Webster, Incorporated

"serpent"
OT:5175
nachash (naw-khawsh'); from OT:5172; a snake (from its hiss):
KJV - serpent.
OT:5172
nachash (naw-khash'); a primitive root; properly, to hiss, i.e. whisper a (magic) spell; generally, to prognosticate:
KJV - certainly, divine, enchanter, (use) enchantment, learn by experience, indeed, diligently observe.
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)

How do we know that this "serpent", written in Genesis 1:1, is Satan?

2 Cor 11:3 But I fear, lest by any means, as the serpent beguiled Eve through his subtilty, so your minds should be corrupted from the simplicity that is in Christ. KJV

Rev 12:9 And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him. KJV


Gen 3:
2 And the woman said unto the serpent, We may eat of the fruit of the trees of the garden:
3 But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.

Eve did know YHVH'S Law concerning the "trees" (people, both of the heavenly and the earthly dimensions) in the garden.

Gen 3:
4 And the serpent said unto the woman, Ye shall not surely die:
5 For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.

Satan was tempting this "innocent" woman, Eve, who had no understanding of deception.

See "Questions Concerning Eve" study on YAH'S TABLE.

Gen 3:
6 And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat.

The words "for food" are in regards to those things that Satan was capable of providing, prducing, and giving unto Eve and unto Adam.

"for food"
OT:3978
ma'akal (mah-ak-awl'); from OT:398; an eatable (includ. provender, flesh and fruit):
KJV - food, fruit, ([bake-]) meat (-s), victual.
OT:398
'akal (aw-kal'); a primitive root; to eat (literally or figuratively):
KJV - at all, burn up, consume, devour (-er, up), dine, eat (-er, up), feed (with), food, freely, in ... wise (-deed, plenty), (lay) meat, quite.
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)


It was Satan's "fruit", which contained his "seeds" ("sperma"), that he was offering. 
Therefore, "the fruit of the tree which is in the midst of the garden" contained Satan's "seeds, which resulted in Eve's conception of Cain in her womb.
Satan's "seeds" could not physically impregnate Adam, but, nonetheless, it spiritually affected him.

Gen 3:
7 And the eyes of them both were opened, and they knew that they were naked; and they sewed fig leaves together, and made themselves aprons.

After this act of disobedience, both Adam and Eve became aware of that which they had done.
They, through their experiences, became cognizant that they were spiritually naked.
They were no longer "covered" by YHVH, because they had opened their minds to Satan's "fruit" (knowledge and abilities), and had opened their bodies to Satan's "seeds".

For the first time, they began to experience "shame". Because they had allowed Satan to expand their knowledge (to open their "spiritual eyes" through these experiences), Adam and Eve were no longer "innocent".

Note that they "sewed fig leaves together" in their ridiculous attempt to hide their "spiritual nakedness" from GOD.

Gen 3:
8 And they heard the voice of the LORD God walking in the garden in the cool of the day: and Adam and his wife hid themselves from the presence of the LORD God amongst the trees of the garden.

Adam and Eve tried to hide themselves among the other peoples (families, people, races which had sprouted from the ground [who had earthly flesh bodies]), and were residing in this protected "garden".

Gen 3:
9 And the LORD God called unto Adam, and said unto him, Where art thou?
10 And he said, I heard thy voice in the garden, and I was afraid, because I was naked; and I hid myself.
11 And he said, Who told thee that thou wast naked? Hast thou eaten of the tree, whereof I commanded thee that thou shouldest not eat?
12 And the man said, The woman whom thou gavest to be with me, she gave me of the tree, and I did eat.
13 And the LORD God said unto the woman, What is this that thou hast done? And the woman said, The serpent beguiled me, and I did eat.

Adam and Eve were attempting to explain away their disobedience unto GOD, The FATHER.
This was neither prudent nor wise, for YHVH knows the hearts of all men.

Adam and Eve had not only unlawfully recieved Satan's "fruit" and "seed", but they were then beginning to put Satan's ways into use, "by attempting to explain away their sins", "by blaming someone else, rather than owning up to that which they had done", and, "by their attempts to lie to 'HE who knows all things', YHVH".

People often try to "cover up" (hide) their own sins. They often try to lie to themselves first, and then to others.
Only YHVH, through YAHSHUA, JESUS CHRIST, can remove their sins, 'if' and 'when' one honestly and earnestly repents of his/her sins.
It is CHRIST who should be the "covering" over our minds... not Satan.

Gen 3:
14 And the LORD God said unto the serpent, Because thou hast done this, thou art cursed above all cattle, and above every beast of the field; upon thy belly shalt thou go, and dust shalt thou eat all the days of thy life:


"the LORD God said unto the serpent" "Because thou hast done this":

"thou art cursed above all cattle, and above every beast of the field"

"cursed"
OT:779
'arar (aw-rar'); a primitive root; to execrate:
KJV - bitterly curse.
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)

"to execrate"
execrate \ek-se-krat\ vb -crated; -crating [L exsecratus, pp. of exsecrari to put under a curse, fr. ex- out of + sacer sacred] : to denounce as evil or detestable; also : detest execration \ek-se-kra-shen\ n
(C) 1995 Zane Publishing, Inc. The Merriam-Webster Dictionary (C) 1994 by Merriam-Webster, Incorporated


Remember: "cattle" and "beast of the field" speaks not only of animals, but can also be used in regards to "people".

YHVH had already sentenced Satan to perish. This sentence was proclaimed in the first heaven age, when Satan commited the "unforgivable sin". Yet, Satan's sentence to perish shall not be carried out until the end of THE LORD'S DAY.

Satan again earned this "curse".
YHVH was denouncing Satan, and his evil and detestable ways, for the sake of HIS (YHVH'S) children, who would have need of coming through this earth age.
This denouncement of Satan could be a forewarning to all.

Gen 3:
15 And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.

"enmity"
OT:342
'eybah (ay-baw'); from OT:340; hostility:
KJV - emnity, hatred.
OT:340
'ayab (aw-yab'); a primitive root; to hate (as one of an opposite tribe or party); hence to be hostile:
KJV - be an enemy.
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)

"seed"
OT:2233
zera` (zeh'-rah); from OT:2232; seed; figuratively, fruit, plant, sowing-time, posterity:
KJV - carnally, child, fruitful, seed (-time), sowingtime.
OT:2232
zara` (zaw-rah'); a primitive root; to sow; figuratively, to disseminate, plant, fructify:
KJV - bear, conceive seed, set with sow (-er), yield.
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)


"it shall bruise thy head, and thou shalt bruise his heel"

Who is this "it shall bruise thy head"?
YAHSHUA, JESUS CHRIST, HIS Government, HIS Ways and Laws of YHVH, HIS Ministry...YHVH'S Truth taught through YAHSUA, JESUS CHRIST, is that which would "bruise" Satan's "head" (his mind, spirit, teaching, ways, his ministry, his seedline, and all who serve him).

"and thou shalt bruise his heel"
How would Satan "bruise" of YAHSUA'S "heel"?

"shalt bruise"
OT:7779
shuwph (shoof); a primitive root; properly, to gape, i.e. snap at; figuratively, to overwhelm:
KJV - break, bruise, cover.
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)


What is HIS "heel"?
OT:6119
`aqeb (aw-kabe'); or (feminine) `iqqebah (ik-keb-aw'); from OT:6117; a heel (as protuberant); hence, a track; figuratively, the rear (of an army):
KJV - heel, [horse-] hoof, last, lier in wait [by mistake for OT:6120], (footstep).
OT:6117
aqab (aw-kab'); a primitive root; properly, to swell out or up; used only as denominative from OT:6119, to seize by the heel; figuratively, to circumvent (as if tripping up the heels); also to restrain (as if holding by the heel):
KJV - take by the heel, stay, supplant, utterly.
OT:6120
`aqeb (aw-kabe'); from OT:6117 in its denominative sense; a lier in wait:
KJV - heel [by mistake for OT:6119].
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)

Satan would cause his evil (his spirit and his evil servants) to pursue all who would follow CHRIST.

Through YAHSHUA'S crucifixion, we have also been shown one example of this "and thou shalt bruise his heel".
It was Satan's servants (who called themselves "Jews", but were not of the tribe of Judah, but of the synagogue of Satan [Revelations 2:9]) which pushed the Roman government to crucify CHRIST.

CRUCIFIXION OF CHRIST
The method of torture and execution used by the Romans to put Christ to death. At a crucifixion the victim usually was nailed to a wooden stake and left to die.

Crucifixion was used by many nations of the ancient world, including Assyria, Media, and Persia. Alexander the Great of Greece crucified 2,000 inhabitants of Tyre when he captured the city. The Romans later adopted this method and used it often throughout their empire. Crucifixion was the Romans' most severe form of execution; so it was reserved only for slaves and criminals. No Roman citizen could be crucified.

Crucifixion involved attaching the victim with nails through the wrists or with leather thongs to a crossbeam attached to a vertical stake. Sometimes blocks or pins were put on the stake to give the victim some support as he hung suspended from the crossbeam. At times the feet were also nailed to the vertical stake. As the victim hung dangling by the arms, the blood could no longer circulate to his vital organs. Only by supporting himself on the seat or pin could the victim gain relief.
But gradually exhaustion set in, and death followed, although usually not for several days. If the victim had been severely beaten, he would not live this long. To hasten death, the executioners sometimes broke the victim's legs with a club. Then he could no longer support his body to keep blood circulating, and death quickly followed. Usually bodies were left to rot or to be eaten by scavengers.

To the Jewish people, crucifixion represented the most disgusting form of death: "He who is hanged is accursed of God" (Deut 21:23). Yet the Jewish Sanhedrin sought and obtained Roman authorization to have Jesus crucified (Mark 15:13-15). As was the custom, the charge against Jesus was attached to the cross; He was offered a brew to deaden His senses, but He refused (Mark 15:23). There was no need for the soldiers to break His legs to hasten death. By the ninth hour (Mark 15:34,37), probably 3:00 P.M.-in only six hours-Jesus was already dead (John 19:31-33). Jesus' body was not left to rot; the disciples were able to secure Pilate's permission to give Him a proper burial.

The cross has been a major stumbling block in the way of the Jews, preventing the majority of them from accepting Jesus as the MESSIAH. The apostle Paul summed up the importance of the crucifixion best: "We preach Christ crucified, to the Jews a stumbling block and to the Greeks foolishness, but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God" (1 Cor 1:23-24). Out of the ugliness and agony of crucifixion, God accomplished the greatest good of all-the redemption of sinners. Also see CROSS.
(from Nelson's Illustrated Bible Dictionary, Copyright (c)1986, Thomas Nelson Publishers)

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"it shall bruise thy head" was spoken unto Satan.

It written in Roman's 16:20 that YAHSHUA, JESUS CHRIST, ("the God of peace") and YHVH'S Truth, would bring about Satan's bruising.

Rom 16:20 And the God of peace shall bruise Satan under your feet shortly. The grace of our Lord Jesus Christ be with you. Amen. KJV