What caused the Fall of Mankind? Was the fall initiated by a transgression of faith, because man trusted the word of the serpent more than the word of God, or was it a transgression of God’s law (an act of disobedience)?

Do different denominations vary on how they answer this question?
It is a common understanding among Christians that Adam and Eve disobeyed God but different groups have different ways of understanding it's role spiritually.


  1 Timothy 2:14 (NIV) And Adam was not the one deceived; it was the
  woman who was deceived and became a sinner.


According to this verse, it suggests that Eve was the one who was deceived by the serpent. Here is an explanation from "Gill's Exposition of the Entire Bible".


  And Adam was not deceived,.... There is no need to say with
  interpreters, that he was not deceived first; and that he was not
  deceived immediately by the serpent, but by Eve; and that he is never
  said in Scripture to be deceived, as Melchizedek is never said to have
  a father or mother. The apostle's positive assertion is to be taken
  without any such limitations or qualifications; Adam never was
  deceived at all; neither by the serpent, with whom he never conversed;
  nor by his wife, he knew what he did, when he took the fruit of her,
  and ate; he ate it not under any deception, or vain imagination, that
  they should not die, but should be as gods, knowing good and evil. He
  took and ate out of love to his wife, from a fond affection to her, to
  bear her company, and that she might not die alone; he knew what he
  did, and he knew what would be the consequence of it, the death of
  them both; and inasmuch as he sinned wilfully, and against light and
  knowledge, without any deception, his sin was the greater: and hereby
  death came in, and passed on all men, who sinned in him: but the woman
  being deceived was in the transgression: and the serpent really
  beguiled her; she owned it herself.


Adam decided to die along with his wife, this makes him the greater sinner.

Answer: The fall of mankind was initiated by the serpent's deception, followed by Eve who believed it, and finally by Adam who sacrificed his own life to share the same fate of his beloved wife. 

This could be a symbol of God's love, who was ready to share our punishment for our sins, who gave His one and only Son, who died on the cross in our stead, bearing all our sins and suffered it's consequences even though He was without sin. Symbolically, Christians are the bride of Jesus Christ, who is also called the Last Adam. Adam gave his life for his wife Eve, and in the same manner, Jesus Christ gave his life for his bride, the Church. The only difference is, while Adam died with his wife but could not save her, Christ saved us through His death.


  Ephesians 5:25 (NIV) Husbands, love your wives, just as Christ loved
  the church and gave himself up for her.
  
  1 Corinthians 15:45(NIV) So it is written: “The first man Adam became
  a living being”; the last Adam, a life-giving spirit.