Who was the author? The apostle Paul wrote the book of Philemon.
What is the book? Philemon is more of a personal letter than the others of Paul that the Holy Spirit saw to it the Church preserved. Philemon was likely the owner of the runaway slave named Onesimus and lived in Colossae, where a congregation probably met in his house.
Where was it written? Paul's letter to Philemon is grouped among the so-called "captivity letters" and so is thought to have been written from Rome during Paul's first imprisonment there.
When was it written? The usual date range for Paul's first Roman imprisonment during which he likely wrote Philemon is A.D. 59-61.
Why? Paul had apparently met up with the runaway slave, Onesiumus, and the letter asks Philemon to both forgive Onesimus and essentially free him to return to Paul.
How? In the letter to Philemon, which was likely transmitted with the letter to the Colossians, Paul is said to follow ancient letter models, first building rapport, then persuading the mind, and finally moving the emotions. The end result is a beautiful illustration of Christian love that is applicable to our guilt and slavery to sin before God, for which Christ mediates our forgiveness that He Himself won on the cross.
For further reading on the book of Philemon:
- Lenski, R. C. H. The Interpretation of St. Paul's Epistles to the Colossians, to the Thessalonians, to Timothy, to Titus and to Philemon. Columbus, Ohio: The Wartburg Press, 1946. (You can find this somewhat dated volume, with its 25 pages of still-helpful comments on Philemon, in our Grace library.)
- Nordling, John G. Philemon, Concordia Commentary: A Theological Exposition of Sacred Scripture. Saint Louis, Missouri: Concordia Publishing House, 2004. (I own a copy of this recent commentary that you are welcome to borrow. The volume's 350 pages seem disproportionately long for the letter's 25 verses, but Nordling does a good job, and, while a scholarly commentary, its format makes it quite accessible.)