One of the most nettlesome challenges in New Testament studies has to do with the dating of the New Testament documents. The letters of Paul are the easiest to date. But a number of scholars believe that some of Paul’s letters are not his (especially Hebrews and the correspondence to Timothy and Titus), thus adding mud to the water. Typically, scholars date the gospels from the late 60s into the 90s of the first century, arguing that Mark is the earliest written and John the latest. The book of Acts was written about the same time that Luke wrote his gospel (perhaps early 80s, although I am aware of a respected scholar who dates Luke-Acts to the 60s). The so-called general epistles are difficult to date (the correspondence from John, Peter, Jude, James) because few hints lie in these letters to events in the authors’ world. Hence, we are left to look at internal factors to try to place these letters in their historical contexts. For instance, Second Peter is not cited by any Christian authors until well into the second century AD; as a result, many scholars date this letter to the early second century and dismiss Peter as its author. But in my view, only an eyewitness (=Peter) could have penned the lines that summarize the experience on the Mount of Transfiguration (2 Peter 1:16-19).
One of the most respected authors, who was a believer and took seriously the evidence from early Christian authors about the New Testament books, was Frederick Fyvie Bruce (he went by the pen-name F. F. Bruce). If I were to recommend one of Bruce’s works, I would suggest his New Testament History, which was first published in paperback in 1972 (the most recent printing was 1983). I find myself regularly rereading parts of that book. He doesn’t spend much time talking about dating matters of New Testament books, but he describes in a very illuminating way the world in which those books were written.
If you want to see how a person deals with issues of dating a New Testament book, you might look at my study where I grapple with dating Mark’s gospel: “The Testimony of Mark,” in Studies in Scripture, Volume Five: The Gospels, edited by Kent P. Jackson and Robert L. Millet (Salt Lake City, Utah: Deseret Book, 1986), 61–87.
I hope that this brief, summarizing answer helps.
Kent Brown