The Abraham Covenant was God's response to human sin. Satan had tempted Eve and then Adam to eat of the forbidden fruit in the Garden of Eden (Gen 3:1-7). The consequence was God's curse; on the woman by pain in childbirth (Gen 3:16) and to Adam on his labours (Gen 3:17). And the universal human curse is death (Gen 3:19).

But God had also placed a curse on Satan and in doing so had pledged himself to overthrow his work (cf Gen 3:15)  In particular Eve's offspring would bruise the Serpent's head. The ESV Study Bible identifies this offspring through Noah 'a righteous man' (Gen 6:9)

From Noah the family line is traced down to Abram.

The Call of Abraham and the Covenant

    Abram was called by God to leave his father's land and go to one God would show him (Gen 12:1)  Along with the Call came a Promise that in Abram all the nations of the earth would be blessed. (Gen 12:2-3)

In faith Abram received and we read later that this was counted as righteousness  (Gen 15:5-6) when God made a Covenant with Abraham (Gen 15:15-18).
The imputation of righteousness was key to the Covenant and to the promise of blessing: that 'blessing' would be of salvation, and of righteousness. ( Rom 10:3-9; 1Cor 1:30) The precious doctrine of justification is thus boxed into too narrow and individualistic terms.* (of which more later)

(N.B.) Much hinges on the understanding of "righteousness". This term is often understood too narrowly.  Easton's Illustrated Dictionary under the heading 'Righteousness' has only a link to 'Justification', on the ground that justification involves the 'imputation...of Jesus Christ' and is identical with salvation. Righteousnesss is often conceived purely as a moral character- God's perfect righteousness, and man's unrighteousness. But it has much more to do with God's character and will to 'put things right', and in face with man's fall and sinfulness and the associated corruption of the whole creation (Rom 8:23). And God's plan is rooted in that wider concept of righteousness which Paul, with his Jewish roots and training would know was in terms of "covenantal faithfulness", and his choice of Abraham and his offspring, with whom he made covenant, purely to put things right. This contains an eschatological element; God would one day intervene again to fulfill that 'putting-all-right' 

It pays to follow the Covenant with Abraham on through OT history and on into the NT

The Covenant with Abraham was renewed with Isaac (Gen 26:3-5) and then he passes the blessing on, even though inadvertently to Jacob (Gen 28:3-4) 
The Covenant with Abraham is further undergirded by that with Moses and the people he had led out of slavery in Egypt. (Exod 24:1-18)  in accord with the earlier covenant (cf Exod 34:27,28) Moses later charges the people to remember the Covenant,with blessings attached for its keeping and curses for breaking it (Deut 28). With the Mosaic Covenant came the Law ('Torah')

  But OT history is of repeated failures of God's people, who were supposed to be for the blessing of the Gentile nations (cf Isa 42:1-7)  With them  he had sworn eternal covenant, and eventually they brought curse upon themselves to the point that they were sent into exile (i) the kingdom of Israel was taken away by Tiglath-Pilesar of Assyria (2 Kings 15:29) (ii) the southern kingdom of Judah failed to learn that lesson and were taken captive in 586BC by Nebuchadnezzar (2 Kings 24:12)

  From all this we learn of God's grace and his faithfulness. He was faithful to his covenant promise and the OT prophets promise a new covenant (eg Jer 31:31-40)  He was faithful too, that even in captivity he promised a return, and eventually a spiritual return (Jer 50:4,5)

Covenant Failure and Fulfillment

  The physical return came in 536BC under Cyrus, king of Persia (2 Chron 26:22,23)  Those who returned knew that spiritually they were still in exile, but a promise had been given by God to Daniel of eventual restoration (cf Dan 9:24-27)  There have been many spurious attempts to use this prophecy to calculate the time of the End. It is worth noting the exact wording of v24:

"Seventy weeks of years are decreed concerning your people and your holy city, to finish the transgression, to put an end to sin, and to atone for iniquity, to bring in everlasting righteousness, to seal both vision and prophet, and to anoint a most holy place"

In the first century AD many Jewish scholars were debating and keenly awaiting the return of Messiah to establish the Kingdom and the Daniel prophecy above all others was quoted. The original Covenant-never reneged on  by God relied on the Law which (a) served to keep the Jews (to an extent) on track and (b) was but the guardian until Christ came (Gal 3:24) And it was at this point of time that a descendant from Abraham came; 'descended according to the flesh' (Rom 1:3)- the Lord Jesus Christ.

The fact is that v24 was fulfilled in an unexpected way in the death on the Cross of the Lord Jesus Christ, who atoned for sin and sealed up righteousness. He was the one faithful Jew, and by his resurrection God's righteous reign was established  This had been foreseen by one who stood as the last of the OT prophets: John Baptist (Mark 1:14,15) He had in the Cross and by his resurrection put all rebellion under his feet and he was established Head of the Church (Eph 1:22) The Church is God's people-of-promise, and heirs to Abraham (Gal 3:29); among those there is no distinction between Jew and 'Greek' (Gentile) (Gal 3:28) The Church was in God's plan from the beginning (cf (Eph 3:4) Paul who had found the futility of the Law considered his keeping of its requirements as filth (Phil 3:7-8) and found his true freedom and salvation in Christ (cf his contrast of the two ways (Gal 2:18-20))

When Jesus died on the Cross, he dealt with the sin-problem. We should remember that his teaching was replete with the Kingdom of God (or heaven). Although the fullness of the Kingdom waits for that day when God makes his final intervention, yet those who believe in Jesus- both Jew and Gentile lived in the Kingdom- yet still in the world. It is a 'now-but-not-yet' situation- a realised eschatology. At that last day the heavenly Assize will pronounce a positive verdict for believers in Jesus- and for them that verdict is already applied- which is 'justification' with a much wider emphasis than a purely individualistic moral issue. Sin is dealt with by God's wider plan, which includes the Cross; includes forgiveness of sin; includes the propitiation of God's wrath. So the Kingdom today is worked out by the indwelling of the Holy Spirit in the believer, and his membership of the church- in which there is neither Jew nor Gentile, for in the Cross the 'middle wall' of hostility was broken down (Eph 2:14-16). And in the church, we become God's co-workers in forwarding his plan.

All who through faith in Jesus as the one single answer to the sin-problem were counted 'in Christ' (Messiah). They were put there by God's doing (1 Cor 1:30) and that secured their right-standing with God (justification), their growth in practical holiness (sanctification) and their eventual eschatological deliverance. In all this we see the fulfillment of Daniel's prophecy. We note that the Kingdom is already here in Christ, but only partly so until Christ's second return and the Great Assize. The favourable verdict of that Assize is already assured for believers (those 'in Christ')- those whose name are in the Book of Life (Rev 20:12,15)

Note on Justification

It is a word from the lawcourt, to declare to be in the right. It is too narrow to concentrate on those passages in Romans, which rightly led to the Reformation and recovery of 'justification by faith' which concentrate, rightly on human sin and God's wrath (cf Rom 1:17)
and the freedom from that wrath through the Cross (Rom 3:21-26)
This is the modern concentration on the individual and misses the majesty of God's plan begun through Abraham and brought to fruition by Jesus.  It also portrays a vengeful God, whose main aim seems to be to indict the guilty sinner, but God is a God who abounds in mercy (Exod 34:6), and takes no pleasure in the death of the sinner (Ezek 18:23)

Abraham: Justification and Covenant

We already note that Abraham believed God's call, and it was counted righteousness. God overlooked Abraham's sin and then confirmed his faith and the promise of a family and nation in a Covenant. 

This faith of Abraham's is the theme of Romans 4, often considered as pointing Abraham as a 'proof case' for justification by faith. This is one reading of Rom 4:3-5. But this missed the real point of all of chapter 4, which is about the bigger picture: God's establishment of his covenant people. Rom 4:11 looks at the giving of the covenant mark of circumcision. and that Abraham received this mark after the ratifying of the covenant (see Gen 15:15-18). But the point that verse 11 makes in this context is that Gentile as well as Jew could 'qualify' for covenant inclusion. Compare this verse:- He received circumcision as a sign or seal of the righteousness which he had by faith while he was still uncircumcised. The purpose was to make him the father of all who believe without being circumcised and who thus have righteousness reckoned to them (RSV) with Gen 17:11 (where the seal of circumcision is given) :- You shall be circumcised in the flesh of your foreskins, and it shall be a sign of the covenant between me and you (RSV) The point is that where Genesis uses 'covenant', Romans uses 'righteousness' In other words justification is the equivalent of covenant-membership. And that was the position after Jesus died on the Cross and God raised him again, The central point at stake is whether we are in God's people; 'in Christ', included in covenant blessing.Yes we are as covenant-members justified as we have believed God's faithfulness just as Abraham. did; whose sin God overlooked because he knew the day would come when he would deal with sins already committed, (Rom 3:25)

The Mosaic Covenant

We have already noted how the Jews in addition to the foundation Covenant with Abraham were given a Covenant with the Torah as its 'condition' Let us look more into this Covenant

After the Exodus from Egypt and the oppression by Pharaoh, the people had passed through the Red Sea (and let's note that Paul in 1 Corinthians 10 says our forefathers. were all baptised into Moses. in the sea (vv1-2)) God led them to Sinai. Here the Covenant (the 'Old Covenant' as, after the writer of Hebrews, we call it) was enacted. This is a covenant proper with the involvement of both parties, a binding together, animal sacrifice, and terms and conditions.
Basically God is offering the people, the nation, a land in which they may dwell, and, if they keep their side of the bargain, where they may dwell in safety. Above all there is the promise that if you obey me fully and keep my covenant. you will be my treasured possession. You will be for me a kingdom of priests and a holy nation (Exod 19:5-6). Then there is the killing of an animal and, significantly, God and Israel become pledged by the sharing of the blood, part of it being sprinkled on the side of the altar and part on the people with the words This is the blood of the covenant the Lord has made with you (Exod 24:8) Herein we see the formal, legal covenant becomes more than that: it is the basis of a relationship.
The blood, the life of the victim has been used to cover the two contracting parties. Each passing under the blood becomes identified with it. Before, they were separate entities; now they are one. So God is a blood-member of Israel. Those last two sentences re key sentences. Let's hold on to them.
There were conditions in the covenant to which the people pledged themselves Exod 34:27-28 contains key words here: Write down these words, for in accordance with these words I have made a covenant with you and with Israel. And he (Moses) wrote on the tablets these words-The Ten Commandments
When two nations made a covenant the terms would have been placed on stone tablets at their border; one stone facing each way and each stone containing the terms and conditions. When Moses came down Sinai with two stone tablets, they didn't contain five command-ments each! When the Ark of Covenant had been built
they were placed there, one tablet facing out, to human view, the other facing inward- for God's presence was between the seraphim on either side of the Ark. Let's hold on to that too.

We've already noted the terms and conditions of the covenant. Like any other covenant, if either party broke it, it would be terminated, only to be renewed if the injured party chose to offer renewal. This covenant was an act of God's choice. All was of God's choosing; he had made them one people; only to their chosen leader did he reveal his Name. So, basically, looked at from the point of view of Israel, we may see the covenant as: If God does something for us, we'll do something for God. So there was no real antithesis between the legal requirements of the covenant and the fact that it was an act of God's grace. Thus it differed from the normal quid-pro-quo nature of normal human covenants

The High Priest

The Law- the Torah was as noted never going to be the way of salvation per se. Rather the inevitable failure of the Jews to keep Torah was to lead to Christ. In the meantime God provided for the people a system of sacrifices, and in these most importantly was 'Yom Kippur'- the Day of Atonement. The act of atonement was the responsibility of the High Priest, who first had to prepare himself before he would enter that part; that inner part, of the Temple specially set apart; that part where God's presence dwelt. The writer of Hebrews reminds us that the first covenant had regulations for worship and also an earthly sanctuary...the priests entered regularly into the outer room to carry on their ministry. But only the high priest entered the inner room, and that only once a year, and never without blood which he offered for himself and for the sins the people had committed in ignorance (Lev 9:1,6) And then the crowds would wait anxiously outside, to see if the Priest would come out alive! The requirements for the Day of Atonement were laid down in Leviticus 16. The High Priest was to take from the (community) two male goats for sin offering and a ram for burnt offering (v5) After offering the ram for his own sin, he would draw lots over the goats. He would enter the Holy Place with a bull's blood, which he would sprinkle, on the Mercy Seat. Then, cleansed from sin, he would re-enter with the goats. One he
would slaughter and would sprinkle the altar with its blood to obtain clean-ness for the people for another year. The second goat: firstly he would lay his hands on it and confess the people's sin on it. Having laid their sins on the goat, it would be driven off into the wilderness, never to return, taking the sins away with it: it was the 'scapegoat' If the priest then emerged alive, they would sigh with relief: the sacrifice had been accepted and their sin covered for another year!

The New Covenant

If, in the Old Covenant, we see the key-point of its institution in the sacrifice of animals, and the sprinkling of blood on the altar (before God) and over the people, then we must look to the shedding of the blood of the Lord Jesus Christ. His death was the sacrifice. (Rom 3:25)
 Here was the sacrifice. Here was the sacrifice presented not by man (according to God’s ordinance) but by God himself. Moses offered the blood of animals to God; Jesus Christ offered his own blood to the Father.
Here his blood is shed over the hearts of those who believe. Actually the phrase ‘sacrifice of atonement’ in the NIV is not a good one. Better is the KJV ‘propitiation’ (the sacrifice which sets aside God’s wrath at our sins), and which completely takes our sin away: ‘atonement’ implies not the removal of our sin, but just it being covered from view. Those who have faith; these are the members of the new covenant people; these are the ones to whom God in Christ pledges himself; these are the ones to whom God says ‘You are my people and I am your God’

The key here is that it’s not what we offer God which ensures our place in the Covenant; it’s not what we provide that pleases him. It is what he provides. But this does produce within the believer’s heart a change. We’ve already looked at the promise of a new covenant in Jer 31:31. If we read on to verse 33 we have this: I will put my law in their minds and write it on their hearts. I will be their God and they will be my people.
Note two things:
1. God puts his law in our minds. No longer is the law an external weight sapping our energy in trying (and not succeeding in) keeping it. It is written into our minds and (on our hearts). It is internal; a wellspring for action; a source of energy.
2. He writes it on our hearts. Actually, the key here is the boundary-treaty. Do you remember that the tablets of the Commandments were placed on the Ark of the Covenant? Well, now the law is placed so that as God looks at our hearts he sees the law and is pleased with its keeping by his Son. As we look out to him, so we see it too. It's there as a constant reminder. The trouble is, we still fail to keep it!
One other point to remember is the mediator of the Covenant. Moses was the mediator of the Old. He it was who sprinkled the blood of the animals on the altar and on the people. He it was who interceded for the people when they made the Golden Calf. But in the New Covenant, Jesus is our Mediator. It was his blood. He sprinkles it on our hearts; he sprinkles it on the heavenly altar. This cup is the new covenant in my blood which is poured out for you (Luke 22:20), he said in words redolent of those spoken by Moses at Sinai. And 1 Tim 2:5 reminds us there is one mediator between God and man, the man Christ Jesus. And Romans 8:34 reassures us that Christ Jesus.is.interceding for us.

Christ, our Great High Priest

This is where we come back to the High Priestly sacrifices on the Day of Atonement. They are no longer required. Heb 8:13 says that by calling the covenant ‘new’ he has made the first one obsolete
Remember that the High Priest had to go into the Most Holy Place once a year for atonement of the people’s sins, first having to offer a sacrifice for his own. Then if he reappeared safe and well, the people knew that God was pleased with the sacrifice and they were O.K. for another year. But it was an unsure, precarious place to be in. If we string together a few verses from Hebrews 9, we will see how absolutely secure we are.
He did not enter by means of the blood of goats and calves; but He entered the Most Holy Place by his own blood, having obtained eternal redemption
How much more then will the blood of Christ, who through the eternal Spirit offered himself unblemished to God cleanse our consciences from acts that lead to death.
For Christ did not enter a man-made sanctuary that was only a copy of the true one; he entered heaven itself to appear for us in God’s presence, (vv 12,14,24)
Jesus Christ presented his blood before his Father in the heavenlies and that is our absolute, cast-iron guarantee. Jesus Christ, through his blood, is the guarantor of our Covenant place with God. 

The 'Old' Covenant, with its laws is now obsolete. We see the sure place we have as members of Christ; 'in Christ'; in the New Covenant. This, surely, is of more reassurance to the sinner than 'justification by faith'. What God looks for is unquestioning belief in the one who brought us this new way. Reformed believers are, of course, standing on solid ground when they place their trust in the Lord Jesus Christ, but the drive of all we have considered is, I propose, in God's wider plan to undo the work of Satan (1 John 3:8) and to make all things new. (Rev 21:5) 

The question of works and God's plan

This may seem an odd diversion. We have seen that our place in God's new community hangs on our trust on Jesus; on his death for our sins and on his resurrection. Our Covenant-place equally is cast-iron guaranteed by our Great High Priest. So far we have not looked at some Scriptures, which cannot be talked away, which tell us that all believers will stand before Christ's Judgment-Seat. (e.g. 2 Cor 5:10; Rom 14:10-12) which make it clear that our 'works' as Christians do count and will be judged. If we know that there is no condemnation in Christ, (Rom 8:1) what are we to conclude?  How do we square the two?
The answer surely must lie in the fact that God placed us in his people 'in Christ', not just for us, but to play our part in his saving purposes. (see Eph 2:10; Phil 2:12-13-in v13 Paul clearly states that God works in us). But doesn't all this rob me of assurance in the certainty of God's Salvation-Plan? The answer lies in the role of the Holy Spirit (Rom 8:5-11), where we are told to live 'by the Spirit'- and if we don't then we are not Christ's anyway. So the final judgment on the true believer will always be positive. Another Romans passage (ch 6) speaks about our incorporation into Christ, and that by this we are 'dead to sin' (Rom 6:2; 5-11). The last verse directly tells you also must consider yourselves dead to sin and alive to God in Christ Jesus (Romans 6:11)  Assurance continues to abound into Romans 8. We know that we are God's children (v14) ; heirs with Christ (v17); assured of 'glorification' (fit for our place in God's glory) (v30). The chapter rounds up  with the fact that Christ himself intercedes for us (v34) and for those 'in Christ' nor anything else in all creation, will be able to separate us from the love of God in Christ Jesus our Lord.(v39-RSV). This means that the Spirit assisting, and working within us will ensure that our verdict will always be a positive one. God's plan of salvation is sure of completion (cf Phil 1:6)

It will be the day of the final establishment of God's Kingdom. It will be the day of the public fulfillment of God's righteousness: the healing of his creation (Isa 11:5-9). The worship of the one true God will be supreme.  God himself will teach us his ways and we will walk in his paths

On that day there will be no more sin, suffering, tears or crying and this will be the final culmination of God's plan to rescue not just errant mankind, but his whole creation.