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At least 13 of the books of the New Testament were written by the Apostle Paul. Of the original 12 Apostles, Matthew, John, and Peter wrote 8 books between them. This leaves 5 to 6 books that were not written by one of the main Apostles: James, Mark, Luke, Acts, Jude, and possibly Hebrews. James: The book of "James" was written by "James, a servant of God and of the Lord Jesus Christ" (James 1:1) This was likely Jesus' brother, 'James the Just', who was a prominent church leader in Jerusalem. Some hold that it was written by a cousin of Jesus, or by James the son of Alphaeus. James the son of Alphaeus (also known as James the Less) was an Apostle, however there is little backing behind the idea he authored "James". James the son of Zebedee, the other Apostle named James, was martyred in 44 A.D and so could not have been the Author (Acts 12:2). James the brother of Jesus is perhaps the most unique author of a Biblical book, as he was not even a disciple of Jesus during His earthly ministry (John 7:5), but became a Christian after the Resurrection (Acts 15:12-21, I Cor 15:6-8, Gal 1:18-19). Though not among the twelve, James was considered an apostle (Gal 1:19). An apostle was one who was sent on a mission, in this case to spread the gospel. Mark: Mark the Evangelist was probably one of the seventy (possibly seventy-two) apostles/disciples sent out by Christ to go before him in his ministry (Luke 10:1-24). Various traditions hold Mark to have been the bishop of Alexandria. Some hold this Mark to be the same as John-Mark mentioned elsewhere in scripture. (Acts 15:36-38). Luke/Acts: Both Luke and Acts were written by Luke. Luke was probably also among the 70 disciples/apostles Jesus sent out. At the very least, he was a disciple of Jesus who was eyewitness to Jesus' ministry (Luke 1:2). Luke was a physician and a historian. Jude: Jude may have been another brother of Jesus, or another relation such as a cousin (Jude 1:1) If he was one of Jesus' brothers, then he probably would not have been a disciple of Christ during his earthly ministry. Possibly, Jude could have been written by Thaddeus, one of the twelve apostles. Hebrews: Hebrews was most likely written by Paul (II Pet 3:15), but there is the possibility it could have been written by one of the other followers of Jesus. S. Michael Houdmann has an excellent answer on that here https://ebible.com/questions/684-who-wrote-the-book-of-hebrews-who-was-the-author-of-hebrews In summary: All the books of the New Testament were written by apostles or disciples of Christ. However, James, Mark, Luke, Acts, Jude, and possibly Hebrews, were not written by the twelve Apostles (counting Paul).
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