Authorship.
The actual letter gives no indication of authorship, but we know that this letter was written well before 90 AD because it was cited in Clement of Rome's letter to the Corinthians (c.96 AD) as the equivalent of Scripture, but never as by Paul, even though he regularly cites Paul and names him. This demonstrates that it was known to have been written by an Apostolic man, someone whose words could be seen as the very words of God, and someone well known to ‘our brother Timothy' (Hebrews 13:23) who was still alive. The latter reference suggests that, if not Paul himself, he probably moved in Paul's circle.
Like 1 John it has no introduction, but moves at once into its theme. The writer does not feel a need to cite his authority to write. And yet it is clearly written to a specific group of people, and there is no evidence of it ever being circulated without that ending, thus it is not does not seem to be just a circulated sermon. Interestingly it ends with a typical Pauline ending, ‘Grace be with you all, Amen', as though Paul, or someone who followed his example, had taken pen in hand to sign off (see 2 Thessalonians 3:17), a practise not found in any other New Testament letters than Paul's (but see 1 Peter 5:14).
Yet its style is not that of Paul, its Greek is smoother and more sophisticated, its way of introducing Scripture quotes is different, and the later uncertainty as to whether Paul wrote it or not, while suggesting Pauline connections, militates against it being directly written by Paul. He may, however, have directly given approval to it.
Its content suggests a Hellenistic Jew, with somewhat like Stephen's viewpoint (Acts 7), or a knowledgeable God-fearer with a sound background in the Septuagint. Eusebius, citing Clement of Alexandria, connects it with Luke as an interpreter/translator of an original Pauline composition written in Hebrew. It is quite clearly not a translation from Hebrew, but perhaps Paul had gathered together some notes in Hebrew which Luke felt very suitable for this particular occasion, and after making their content his own, took and expanded on, putting them in his own words, although possibly under Paul's guidance and approval. It would enable the bearer to cite Paul's authority while naming Luke as the author.
As we note from the acceptance of his Gospel and the Acts of the Apostles Luke's credentials would be accepted. Tertullian describes it as though he had received a tradition that it was written by Barnabas, but there is no further evidence of this. Whoever it was, Luke, Barnabas, Apollos, Silas (Silvanus) or the like, it was seen as sufficiently authoritative to be received and cited by a prominent elder in the church in Rome (Clement of Rome - who presumably did know who wrote it, and probably expected the Corinthians to know) at the end of 1st century AD.
Theme.
It begins immediately with the emphasis that God has over the ages spoken to the world through the prophets, and then goes on to describe God's final revelation of Himself through One who was, unlike them, a Son, One Whom He describes as a full and true portrayal of God's glory and power, a royal figure (He sits at God's right hand), and a High Priest (He makes purification for sins).
This One is shown to be greater than the angels, greater than Moses, greater than Joshua, and greater than Aaron, the earthly High Priest and as introducing a greater deliverance than all. Thus He is greater than all whom the Jews saw as great in their great previous deliverance at the Exodus. He is the new Deliverer. He is seen as having through the sacrifice of Himself replaced the sacrificial system, which had merely pointed ahead to His coming, making by the sacrifice of Himself a means by which those who are His can be sanctified and perfected, and providing for them a way into the presence of God.
Thus they must recognise that there is now acceptance with God by no other way. And his readers are urged to ensure that they continue their faith in Him right through to the end in order that they might be saved.
By the end of the second century AD it bore the heading ‘To The Hebrews', and its message would certainly be applicable to Jewish Christians or converted God-fearers who were considering lapsing back to Judaism, possibly because of persecution, and because they were subsequently persuading themselves that the God-revealed religion of the Jews would surely be sufficient for salvation, while avoiding the tribulations of being a Christian. But its message rejects such an idea on the grounds that Judaism has now been replaced in Christ, which means that it is based on heavenly realities and not on earthly shadows. And being based firmly on an interpretation of the Old Testament, the letter has a message for all.
A good case can be made for it being seen as written to a small church grouping composed of mainly Greek speaking converted Jewish priests and Pharisees, who had become rather inward looking and were practising their own form of Jewish Christianity, some of whom, in the face of extreme pressure and persecution were speaking of turning from Christ and returning again to Judaism. It may well be that some who knew them had asked the writer to use his recognised authority to plead with them to think again.
That he did so on the basis of his very accurate knowledge of Old Testament teaching rather than on a general knowledge of Judaism comes out in the letter. And the lack of any mention of the destruction of the temple may well suggest a date before 70 AD.