Hebrews 1-4.
The "Epistle to the Hebrews" presents a puzzle, because no early manuscript contains the name of the author, or of the adressee.
An early Bishop of Rome, Clement, thought that Paul must have written it in Hebrew, and got Luke to translate it into Greek.
Tertullian, writing at the very beginning of the Third Century, thought that it was written by Barnabas.
Martin Luther put forward the idea that it was written by Apollos.
The English scholar and archeologist, Dr. Ramsey, prosed that it was written by Philip
The German theologian Hernack, made the startling suggestion that it was written by Priscilla, which might make it easier to explain why the author's name was removed from early documents. This argument is developed in the Wikipedia reference.
Some have suggested, on the basis of its elegant, well-thought out Greek,, that it is not a letter at all, but a transcript of an early sermon, which would make it the only complete sermon to have survived from the early church. The record of Stephen's partial sermon in Acts is rather similar.
When was it written
The author spends much time arguing that temple ritual had been superseded. However, the destruction of the temple is not mentioned, suggesting that the letter was written before 70 AD. Clement quotes from it in around 90 AD
To whom was it written?
The only direct hint is the mention of "those who are from Italy" at the end of the letter, perhaps indicating that the letter was written to Rome.
The heavy emphasis on arguments that Jesus outranks all other authorities, inlcuding angels, reminds many of the arguments against Gnostics (or proto-Gnostics) in Colossians, suggesting that it was written for a similar purpose.
its focus on Jews suggests that it was written to a Jewish community. One suggestion has been that it is addressed to a community of Jewish ex-priests, (mentioned in Acts 6) under pressure to return to the temple.
Other suggestions have been Jewish Christians, disappointed by the non-arrival of the Second Coming, tempted to return to orthodox Judaism.
Other Jewish Christians may need instruction on the universalist aspect of Christianity, as against the nationalistic Judaism of c. 60 AD.