Adam Clarke on Deuteronomy 17:18

He shall write him a copy of this law - משנה התורה הזאת mishneh hattorah hazzoth, an iteration or duplicate of this law; translated by the Septuagint, το δευτερονομιον τουτο this deuteronomy. From this version both the Vulgate Latin and all the modern versions have taken the name of this book; and from the original word the Jews call it Mishneh. See the preface to this book.

Out of that which is before the priests the Levites - It is likely this means, that the copy which the king was to write out was to be taken from the autograph kept in the tabernacle before the Lord, from which, as a standard, every copy was taken and with which doubtless every copy was compared; and it is probable that the priests and Levites had the revising of every copy that was taken off, in order to prevent errors from creeping into the sacred text.