Most people are aware that the Bible is divided into two major parts called Old Testament and New Testament.  This is done for other than just some sort of convenience.
In the Old Testament, Genesis covers the creation and early history of God's dealings with man down to the time of the bondage of Israel in Egypt.  From the end of their bondage, the Law of Moses is God's guidance for the Israelite nation.  Books of history, poetry, prophecy and doctrine thus make up the volume of the Old Testament.  The record ends about 400 years before Christ.  At times the Old Testament is referred to in the New Testament as the Old Covenant, Old Law, the Law and the Prophets, or the Law, Psalms and the Prophets or just the Law.  
The New Testament is referred to as law, identified also as the New Covenant, will, testament, and even the gospel.  It contains the fulfillment of God's plan of redemption for man prophesied in the Old Testament.  It begins with the life of  Jesus the Christ followed by some history of the early church.  It is mostly composed of doctrinal works by inspired men.  
The Old Testament was temporary as the basis of faith and practice. The Law of Moses was primarily created for the descendants of Abraham, the Israelite nation.  The purposes for its existence as law were fulfilled.  
We are now under a new covenant, a superior covenant, created for all men.  It reveals the bases for the remission of sins.  It provides access to God and defines faithful service toward Him.
This New Covenant was foretold in the Old Testament, Jeremiah 31:31-32—
"Behold, the days come, saith the Lord, that I will make a new covenant with the house of Israel, and with the house of Judah: Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the Lord."
This was fulfilled.  Hebrews 8:6 speaks of the new covenant as a "better" covenant—
"But now hath he obtained a ministry the more excellent, by so much as he is also the mediator of a better covenant, which hath been enacted upon better promises."
Following this, begining with verse 8, the passages from Jeremiah 31:31ff are quoted, as above.
The Old Law, and all related to it, was not intended to last; it was temporary.  It was not intended for the gospel system, so a clear contrast is given in scripture.  That is why Paul said in Galatians 2:16 that "by the works of the law shall no flesh be justified," and in Galatians 5:4, "Ye are severed from Christ, ye who would be justified by the law; ye are fallen away from grace."
This difference is seen again in Galatians 3:24-25, where the Law of Moses and the gospel of Christ (Faith) are contrasted.  The law served its purpose and then its authority ceased—
"So that the law is become our tutor to bring us unto Christ, that we might be justfied by faith.  But now that faith is come, we are no longer under a tutor."
This difference is again contrasted in Galatians 3:21-31, under an allegory of Hagar and Sarah.  It emphasizes that we are no longer under the old law, but rather a new one.
Hebrews 7:12 says, after establishing Jesus is our high priest—
"For the priesthood being changed, there is made of necessity a change also of the law."
He continues in verses 18 and 22—
"For there is a disannulling of a foregoing commandment because of its weakness and unprofitablness (for the law made nothing perfect), and a bringing in thereupon of a better hope, through which we draw nigh unto God . . . by so much also hath Jesus become the surety of a better covenant."
Hebrews 10:9-10 add this—
Then hath he said, Lo, I am come to do thy will.  He taketh away the first that he may establish the second.  By which will we have been sanctified through the offering of the body of Jesus Christ once for all."
This ending of the Old Law includes even the Ten Commandments as a set of laws for us; they are inadequate for the Christian.  That does not mean we can steal, murder, etc., for the New Testament forbids that, and more.  The New Testament commands go further than the Ten Commandments.  To emphasize this point, first note I Kings 8:9, 21—
"There was nothing in the ark save the two tables of stone, which Moses put there at Horeb, when the Lord made a covenant with the children of Israel, when they came out of Egypt. . . And I have set there a place for the ark, wherein is the covenant of the Lord, which he made with out fathers, when he brought them out of the land of Egypt."
At that time, the ark of the covenant contained only the two tables of the Ten Commandments.  Those tables are described as the covenant God made with Israel when they came out of Egypt.  Recall that Jeremiah 31:31-32, as we have already read, says that God would make a new covenant, not like the one He made with them when he brought them out of Egypt.  This was fulfilled in the New Testament.
This is why II Corinthians 3:7-16 speaks of the Ten Commandments as the ministration of death as versus the new law the ministration of life.  They were the ministration of death because there was no provision for life in them.  Paul argues specifically about the abolishment of the old covenant, including the Ten Com-mandments.  See this as well in Colossians 2:14, 16—
"having blotted out the bond written in ordinances that was against us, which was contrary to us: and he hath taken it out of the way, nailing it to the cross. . . Let no man therefore judge you in meat, or in drink, or in respect of a feast day or a new moon or a sabbath day."
The sacrifices ended, but also did the yearly, monthly, and weekly observances, such as the Sabbath, one of the Ten Commandments.  We have a new day of observance now, the first day of the week, commemorating the day of the Lord's resurrection.  We cannot go back to the Old Law and justify our religious practice and worship today.  We are under a new law, a better law, based on better promises.  
Not finding authority in the New Testament, many people run to the Old Testament for authority for what they do in religion; burning incense, priestly garb, feast days, instrumental music in worship, laughing, dancing and shouting in worship and many other things they want.  However, like circumcision that Paul spoke of in Galatians 5, we are severed from Christ if we seek to be justified by the law.  Our authority is the New Testament of Jesus Christ, not the Old Testament.  The latter has been taken out of the way.
This does not mean, however, that the Old Testament has no value; it has great value.  It reveals the orgins of man and this world.  It shows God's plan of redemption for man following the fall.  It details that plan in God's handling of Israel and the nations.  It proves, by fulfillment of prophecy, the person of Christ and what He did for our salvation.  It shows just who Jesus is by nature; He is one of the Godhead, God come in human form.  We could not understand some of the things said in the New Testament without a background in the Old Testament; the book of Hebrews shows this point.  Romans 15:4—
"For whatsoever things were written aforetime were written for our learning, that through patience and through comfort of the scriptures we might have hope."
Hebrews 11 relates numerous examples from the Old Testament of the kind of faith that pleases God, an obedient faith.  We are not commanded to do what those people did then, but we must obey God in what He tells us to do now, under the New Testament, with the same firm conviction.  There is the difference, in regard to authority, between the Old and the New!  
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