What Is The Purpose Of The Book Of Mormon?

From Mormon.org

To convince Jew and Gentile that Jesus is the Christ and the Savior of the world

"to the convincing of the Jew and Gentile that Jesus is the Christ, the Eternal God" ("Title Page of the Book of Mormon")

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the Book of Mormon exists to bear witness of Jesus Christ—who He is, what He taught, why He died, and His resurrection from the dead. There are more than 6,000 verses in the Book of Mormon. Nearly 4,000 of those verses mention Jesus. 

The culminating event in the Book of Mormon is the appearance of Jesus Christ sometime shortly after His Resurrection in the old world to a group of people living in the Americas (3 Nephi 11).  ("What is the Book of Mormon About?", 7 Dec 2017)

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The major mission of the Book of Mormon, as recorded on its title page, is ‘to the convincing of the Jew and Gentile that Jesus is the Christ, the eternal God, manifesting himself unto all nations.’ 

“The honest seeker after truth can gain the testimony that Jesus is the Christ as he prayerfully ponders the inspired words of the Book of Mormon.
“Over one-half of all the verses in the Book of Mormon refer to our Lord. Some form of Christ’s name is mentioned more frequently per verse in the Book of Mormon than even in the New Testament. 

“He is given over one hundred different names in the Book of Mormon. Those names have a particular significance in describing His divine nature
(“Come unto Christ”, Ezra Taft Benson,  Oct 1987)

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[Isaiah] verily saw my Redeemer, even as I [Nephi] have seen him.
And my brother, Jacob, also has seen him as I have seen him; wherefore, I will send their words forth unto my children to prove unto them that my words are true. Wherefore, by the words of three, God hath said, I will establish my word. Nevertheless, God sendeth more witnesses, and he proveth all his words.
Behold, my soul delighteth in proving unto my people the truth of the coming of Christ
(2 Nephi 11:3)

To persuade people to come unto Christ and be saved

"the fulness of mine intent is that I may persuade men to come unto the God of Abraham, and the God of Isaac, and the God of Jacob, and be saved." 1 Nephi 6:4

To show that God fulfills all his promises that he makes to his children. (To increase faith in God)

"to show unto the remnant of the house of Israel what great things the Lord hath done for their fathers" ("Title Page of the Book of Mormon")

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"that they may know the covenants of the Lord" ("Title Page of the Book of Mormon")

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That the readers and their peoples "might not be destroyed" 
See "Title Page of the Book of Mormon"

Moroni has seen two peoples of the Lord be eliminated from the earth. He is warning us on how to not repeat what they did.