Moses is the central author
The opening of Deuteronomy introduces the book as words Moses spoke to Israel east of the Jordan, shortly before the people entered the promised land. Much of the book consists of his final teaching, reminders, warnings, and covenant instruction for a new generation of Israelites (Deuteronomy 1:1-5).
Deuteronomy also says plainly that Moses wrote the law and gave it to the priests and Israel's elders. Later, it says he finished writing the words of that law in a book (Deuteronomy 31:9, Deuteronomy 31:24). For that reason, Jewish and Christian tradition has long identified Moses as Deuteronomy's main author.
And Moses wrote this law, and delivered it unto the priests the sons of Levi, which bare the ark of the covenant of the Lord, and unto all the elders of Israel.
What did Moses write?
The word Deuteronomy means second law, though the book is not simply a duplicate of earlier laws. Moses restates God's covenant for Israel as they prepare to live in Canaan. He calls them to love the Lord wholeheartedly, reject idolatry, practise justice, and remember God's faithfulness (Deuteronomy 6:4-5, Deuteronomy 10:12-13).
Jesus treated Moses' writings as a witness pointing to him. He told his hearers that believing Moses would lead them to believe Jesus too, because Moses wrote of him (John 5:46-47). That does not settle every modern question about editing or compilation, but it shows the weight Jesus gave to Moses' written testimony.
Hear, O Israel: The Lord our God is one Lord: And thou shalt love the Lord thy God with all thine heart, and with all thy soul, and with all thy might.
What about Moses' death in chapter 34?
There is one obvious detail. Deuteronomy ends by describing Moses' death, burial, and Israel's mourning for him (Deuteronomy 34:5-8). Moses could not have written that account after he died.
Many readers therefore understand Moses to have written the main body of Deuteronomy, while a later inspired writer added the final account. The Bible does not identify that writer, so it is wise not to be more certain than Scripture is. The ending honours Moses, but it also makes clear that God's work did not end with him.
Read Deuteronomy as Moses' farewell
Deuteronomy comes alive when you read it as the farewell teaching of an aged leader who knows he will not cross the Jordan. Moses speaks urgently because Israel is about to face new pressures, new temptations, and a new land.
His central call is still clear: remember who God is, trust him, and shape everyday life around loving him. As you read, notice how often Moses points back to God's rescue of Israel and forward to the need for faithful obedience (Deuteronomy 8:11-14).