Theology and Politics from a Conservative, Biblical Perspective
This book, more than any other, was the book that our Lord quoted from most often. That alone tells us how very important this book is for us. However, this does not diminish the value and importance of other books of the Bible. It is likely that Deuteronomy was a favorite of Jesus because of all the Law that it dealt with and the application of that Law.
Remember Jesus came to fulfill the Law at all points in order to become a worthy sacrifice for you and me. This He did because He was steeped in the actual Law, not tradition. He was able to deftly distinguish between tradition and the Law, thereby ignoring man-made rules and regulations in favor of fulfilling the specificity of the Law as given by God originally to Moses. Jesus was also able to call out the religious leaders because of the way they often hid behind tradition while ignoring the Law itself.
The name of the book comes from the Septuagint, which means, “the second.” This refers to the fact that the Law, originally given and received in the book of Exodus, was repeated here in Deuteronomy. However, as noted, it goes beyond simple repetition of the Law as given and moves into the area of application for the Israelites.
One commentator on the book of Deuteronomy notes that Deuteronomy, “is a call to the service of one God by an elect people centered around one sanctuary, through obedience to the law in the land which God has given.” 
The author is again Moses and the book of Deuteronomy is filled with his sermons where he applies the Law to the various aspects of daily life for the Israelites.
It is difficult to rationally deny that Moses wrote Deuteronomy. Dr. Thomas L. Constable makes the following statements regarding Mosaic authorship.
The Mosaic authorship of this book is quite easy to establish. The book claims to be the words of Moses (1:5, 9; 5:1; 27:1, 8; 29:2; 31:1, 30; 33:1, 30) and his writing (31:9, 22, 24). Other Old Testament books also assert the Mosaic authorship of Deuteronomy
(1 Kings 2:3; 8:53; 2 Kings 14:6; 18:6, 12). Jesus Christ believed that Moses wrote Deuteronomy (Matt. 19:7-8; Mark 10:3-5; 12:19; John 5:46-47), as did the Apostle Peter (Acts 3:22), Stephen (Acts 7:37-38), Paul (Rom. 10:19; 1 Cor. 9:9), and the author of the
Epistle to the Hebrews (Heb. 10:28). 
The book Deuteronomy occurs roughly 1,445 BC to 1,400 BC and occurs near the borders of Canaan.
As with all books of the Bible, Deuteronomy can be outlined and broken down in several ways.
Constable provides a very detailed outline of the book as well as this simpler outline:
Interestingly enough, as Moses reviewed the Law and the Covenants, he not only encouraged the Israelites to obey God in all things, but to love Him (5:9-10; 6:4-5; 7:9; 10:12-13; 11:1, 13-14, 22-23; 13:1-13, esp. vv. 1-3; 19:8-9). This concept was likely largely unknown to the Israelites who did not necessarily love any idols they may have worshiped before Jehovah, but simply worshiped them out of fear and/or to gain something from them.
The idea to love God was foreign to the Israelites’ way of life and understanding. It is something that needed to be developed within them. Why did Moses urge the Israelites to love God? Simply because love – true love – creates a desire to please the object of that love, from the heart. Without love, things done for another are done mainly out of fear or duty. Moses wanted the Israelites to go well beyond this where God was concerned. He wanted them to love God so that their actions and words toward Him would flow from a heart overflowing with appreciation and awe.
It is also important to understand that love creates a different relationship, one that is ultimately established on trust, not selfish gain. What Moses taught the Israelites then is just as important now for Christians. We should revere God because of who He is and the power that He wields. We should love Him because He first loved us and has granted so many blessings made possible because of the selfless act of love evidenced by Jesus, God the Son, in living a life of sinless perfection, which made Him worthy to offer Himself as a propitiation for your sin and mine.
The fact that God wants us to relate to Him on the foundation of love speaks volumes about His own love for us and His lack of arrogance and anger for the objects of His love. For those who remain outside the bounds of His love, there is nothing but eternal wrath in store for them. This is not what God wants but will allow for those who are resolute in refusing His love toward them.
Deuteronomy was a book our Lord quoted from often. In it are treasures regarding the reiteration of the Law and how, by loving God, we are apt to obey Him and His Law more easily and readily, not out of duty.
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 (Deuteronomy 6:4-5; KJV).
 http://www.soniclight.com/constable/notes/pdf/deuteronomy.pdf, p. 1
 Ibid, pp. 1-2