Irenaeus on the Gospels

Here is a following excerpt from Irenaeus on the four canonical Gospels.

We have learned the plan of our salvation from no one else than the ones through whom the gospel has come down to use. At first, they proclaimed it in public, but later on, in accordance with Go'd will, they handed it down to us in the Scriptures, to be the ground and pillar of our faith. It is unlawful to assert that they preached before they possessed 'complete knowledge', as the heretics dare to say, who boast that they have improved on the apostles. After our Lord rose from the dead, the apostles received power from on high when the Holy Spirit came down upon them, were filled with all gifts, and thus received complete knowledge. They departed to the ends of the earth, preaching the glad tidings of the good things sent from God to us, and proclaiming the peace of heaven toward humankind. They all equally and individually possessed the gospel of God. Matthew produced a written gospel for the Hebrews in their own language, while Peter and Paul were preaching at Rome, laying the foundations of the church there. After their departure, Mark, the disciple and interpreter of Peter, handed down to us in writing what Peter had preached. Luke also, the companion of Paul, recorded in a book the gospel Paul preached. Afterwards, John, the disciple of the Lord, who had leaned upon his breast, also published a gospel while he was living at Ephesus. (Against Heresies, 3.1.1)

Here are some thoughts on the composition of the Gospels according to Irenaeus.

1. Matthew's Gospel is originally composed in Hebrew
2. Mark wrote his gospel after Peter and Paul left Rome
3. Mark composed Peter's preaching (Mark 1.1?)
4. Luke composed the "gospel Paul preached"
5. John wrote his Gospel while in Ephesus

Here Irenaeus explains the various themes of each Gospel:

The gospels we have comport with these descriptions. John tells of his original, effectual, and glorious generation from the Father, declaring: 'In the beginning was the Word, and the Word was with God, and the Word was God'; also, 'All things came into being through him, and without him not one thing came into being'. This is also why his gospel is full of confidence, for that is who he was. Luke focusses on his priestly character: he begins his gospel with Zechariah the priest offering sacrifice to God—for now the fatted calf is ready, which will be sacrificed in order to bring the younger son home. For his part, Matthew declares his generation as a man, beginning his gospel with 'An account of the genealogy of Jesus the Christ, the son of David, the son of Abraham', and 'Now the birth of Jesus the Christ took place in this way'. His is the gospel of his humanity; for which reason it is, too, that a humble and meek man is kept up through the whole Gospel. Mark, on the other hand, begins with the prophetical spirit coming down from on high to people: 'The beginning of the good news of Jesus Christ, the Son of God, as it is written in the prophet Isaiah... (Against Heresies 3.11.8)

According to Irenaeus, the themes of each Gospel are:

1. Matthew — Humanity
2. Mark — Prophetic
3. Luke — Sacredotal
4. John — Glorious generation of the Father