Muratorian canon is list of New Testament books discovered it in Ambrosian library in around 1740. We may never know who wrote it – it was named after the person who discovered it, Lodovico Antonio Muratori (1672 to 1750). The front and end parts of the list were torn (and lost), what remains reads (English translation from The Anti Nicene Fathers, Vol. 5, page 603):
…..those things at which he was present he placed thus, The third book of the Gospel, that according to Luke, the well-known physician Luke wrote in his own name in order after the ascension of Christ, and when Paul had associated him with himself as one studious of right. Nor did he himself see the Lord in the flesh; and he, according as he was able to accomplish it, began his narrative with the nativity of John. The fourth Gospel is that of John, one of the disciples. When his fellow-disciples and bishops entreated him, he said, “Fast ye now with me for the space of three days, and let us recount to each other whatever may be revealed to each of us.” On the same night it was revealed to Andrew, one of the apostles, that John should narrate all things in his own name as they called them to mind. And hence, although different points are taught us in the several books of the Gospels, there is no difference as regards the faith of believers, inasmuch as in all of them all things are related under one imperial Spirit, which concern the Lord’s nativity, His passion, His resurrection, His conversation with His disciples, and His twofold advent,-the first in the humiliation of rejection, which is now past, and the second in the glory of royal power, which is yet in the future. What marvel is it, then, that John brings forward these several things constantly in his epistles also, saying in his own person, “What we have seen with our eyes, and heard with our ears, and our hands have handled, that have we written. For thus he professes himself to be not only the eye-witness, but also the hearer; and besides that, the historian of all the wondrous facts concerning the Lord in their order.
Moreover, the Acts of all the Apostles are comprised by Luke in one book, and addressed to the most excellent Theophilus, because these different events took place when he was present himself; and he shows this clearly i.e., that the principle on which he wrote was, to give only what fell under his own notice-by the omission of the passion of Peter, and also of the journey of Paul, when he went from the city-Rome-to Spain.
As to the epistles of Paul, again, to those who will understand the matter, they indicate of themselves what they are, and from what place or with what object they were directed. He wrote first of all, and at considerable length, to the Corinthians, to check the schism of heresy; and then to the Galatians, to forbid circumcision; and then to the Romans on the rule of the Old Testament Scriptures, and also to show them that Christ is the first object in these;-which it is needful for us to discuss severally, as the blessed Apostle Paul, following the rule of his predecessor John, writes to no more than seven churches by name, in this order: the first to the Corinthians, the second to the Ephesians, the third to the Philippians, the fourth to the Colossians, the fifth to the Galatians, the sixth to the Thessalonians, the seventh to the Romans. Moreover, though he writes twice to the Corinthians and Thessalonians for their correction, it is yet shown i.e., by this sevenfold writing-that there is one Church spread abroad through the whole world. And John too, indeed, in the Apocalypse, although he writes only to seven churches, yet addresses all. He wrote, besides these, one to Philemon, and one to Titus, and two to Timothy, in simple personal affection and love indeed; but yet these are hallowed in the esteem of the Catholic Church, and in the regulation of ecclesiastical discipline. There are also in circulation one to the Laodiceans, and another to the Alexandrians, forged under the name of Paul, and addressed against the heresy of Marcion; and there are also several others which cannot be received into the Catholic Church, for it is not suitable for gall to be mingled with honey.
The Epistle of Jude, indeed, and two belonging to the above-named John or bearing the name of John are reckoned among the Catholic epistles. And the book of Wisdom, written by the friends of Solomon in his honour. We receive also the Apocalypse of John and that of Peter, though some amongst us will not have this latter read in the Church. The Pastor, moreover, did Hermas write very recently in our times in the city of Rome, while his brother bishop Plus sat in the chair of the Church of Rome. And therefore it also ought to be read; but it cannot be made public in the Church to the people, nor placed among the prophets, as their number is complete, nor among the apostles to the end of time. Of the writings of Arsinous, called also Valentinus, or of Miltiades, we receive nothing at all. Those are rejected too who wrote the new Book of Psalms for Marcion, together with Basilides and the founder of the Asian Cataphrygians. ….
The list has four Gospels (it refers Luke as the third Gospel, then the torn and lost front part most likely has Matthew and Mark as the first two Gospels), Acts, thirteen Paul epistles with the order: Corinthians (2 epistles), Ephesians, Philippians, Colossians, Galatians, Thessalonians (2 epistles), Romans, Philemon, Titus and Timothy (2 epistles), followed by Jude, 1 & 2 John, Wisdom of Solomon and Apocalypse (Revelation) of John and of Peter. Apocalypse of Peter, which was not accepted by some, no longer belongs to New Testament, while Wisdom of Solomon is now part of (Catholic and Orthodox) Old Testament. The inclusion of Wisdom of Solomon is unusual, though Epiphanius (c. 315 to 402 AD), bishop of Salami in Cyprus, also included both Wisdom and Sirach in his list of New Testament books (cf. Adversus Haereses or Panarion (Medicine Chest) 76 Conf. Act 5 p. 941). Muratorian list does not have James, Hebrews, 1 & 2 Peter and 3 John. The compiler mentioned two other Pauline epistles, to the Laodiceans (cf. Colossians 4:16) and to the Alexandrians, which he claimed to be forged. He also mentioned Shepherd of Hermas, which can be read but not to be given to people.
Based on the statement “The Pastor, moreover, did Hermas write very recently in our times in the city of Rome, while his brother bishop Plus sat in the chair of the Church of Rome“, Muratorian list was dated in third quarter of second century AD because the pontificate of Pius I was from c. 140 to 154 AD. If this is the case then it is the earliest known list of New Testament books. The dating has been challenged because it is unlikely Christians started defining canon of New Testament in second century when they started defining that of Old Testament in fourth century (Refer to Hahneman, G.M.: The Muratorian Fragment and the Development of the Canon).