John Calvin (updated)

Since Calvin's prominence is widely known, I will not waste time introducing him.  His theology casts a large shadow over the rest of Reformed theology for the next two centuries and beyond.  He teaches essentially the same doctrine of the covenant as Bullinger and Zwingli.  This is especially true in terms of his doctrine of the Mosaic covenant as essentially a covenant of grace.  Like Bullinger and Zwingli, Calvin's doctrine is formulated over against the radical tendencies of the Anabaptists of the period.  Furthermore, the views of Michael Servetus, a nemesis of Calvin's, also come into view.  We hope to provide some excerpts from Servetus in the future. 
 
Calvin deals with this subject in many places in his writings.  In time, we will try to provide broad selections from many of his works.  For starters, one should consult the section of his Institutes that deals with the similarities between the Old and New Testaments.  If you don't already have it in your library, you can read it here.  Here is the substance of his view:
And, indeed, both these topics may be despatched in one word. The covenant of all the fathers is so far from differing substantially from ours, that it is the very same; it only varies in the administration. But as such extreme brevity would not convey to any man a clear understanding of the subject, it is necessary, if we would do any good, to proceed to a more diffuse explication of it. But in showing their similarity, or rather unity, it will be needless to recapitulate all the particulars which have already been mentioned, and unseasonable to introduce those things which remain to be discussed in some other place. We must here insist chiefly on three principal points. We have to maintain, First, that carnal opulence and felicity were not proposed to the Jews as the mark towards which they should ultimately aspire, but that they were adopted to the hope of immortality, and that the truth of this adoption was certified to them by oracles, by the law, and by the prophets. Secondly, that the covenant, by which they were united to the Lord, was founded, not on any merits of theirs, but on the mere mercy of God who called them. Thirdly, that they both possessed and knew Christ as the Mediator, by whom they were united to God, and became partakers of his promises (Institutes, II.x.2)
Admittedly, there are times in Calvin's writings where he speaks of the peculiar ministry of Moses with reference to the law in a different way.  This often appears in his analysis of the Pauline epistles.  However, Calvin's comments in his Institutes with regard to this aspect of his teaching needs to be heeded:
"Paul was disputing with perverse teachers who pretended that we merit righteousness by the works of the Law. Consequently, to refute their error he was sometimes compelled to take the bare Law in a narrow sense, even though it was otherwise graced with the covenant of free adoption."  (II.vi.2)
In other words, if we abstract the Mosaic law out of its true place in the covenant of grace, we end up with something substantially distinct from a covenant of grace.  This is what the Pharisees did, and Paul takes them to task for it. 
 
Furthermore, we must also note that some recent writers have tried to argue that Calvin viewed the Mosaic covenant as a covenant of works.  How this idea fits with the following quotation is beyond us:

Now, as to the new covenant, it is not so called, because it is contrary to the first covenant; for God is never inconsistent with himself, nor is he unlike himself, he then who once made a covenant with his chosen people, had not changed his purpose, as though he had forgotten his faithfulness. It then follows, that the first covenant was inviolable; besides, he had already made his covenant with Abraham, and the Law was a confirmation of that covenant. As then the Law depended on that covenant which God made with his servant Abraham, it follows that God could never have made a new, that is, a contrary or a different covenant. For whence do we derive our hope of salvation, except from that blessed seed promised to Abraham? Further, why are we called the children of Abraham, except on account of the common bond of faith? Why are the faithful said to be gathered into the bosom of Abraham? Why does Christ say, that some will come from the east and the west, and sit down in the kingdom of heaven with Abraham, Isaac, and Jacob? (Luke 16:22; Matthew 8:11) These things no doubt sufficiently shew that God has never made any other covenant than that which he made formerly with Abraham, and at length confirmed by the hand of Moses. This subject might be more fully handled; but it is enough briefly to shew, that the covenant which God made at first is perpetual (Calvin on Jeremiah 31).

Commenting on Ephesians 2:12, Calvin also seems to equate the covenant given through Moses in the two tables with the Abrahamic covenant.  The full comment is included in order to provide context. 

12. That at that time ye were without Christ. He now declares that the Ephesians had been excluded, not only from the outward badge, but from everything necessary to the salvation and happiness of men. As Christ is the foundation of hope and of all the promises, he mentions, first of all, that they were without Christ. But for him that is without Christ, there remains nothing but destruction. On Him the commonwealth of Israel was founded; and in whom, but in Himself, could the people of God be collected into one holy society?

A similar observation might be made as to the tables of the promise.  On one great promise made to Abraham all the others hang, and without it they lose all their value: “In thy seed shall all the nations of the earth be blessed." (Genesis 22:18.) Hence our apostle says elsewhere, “All the promises of God in him are yea, and in him Amen.” (2 Corinthians 1:20.) Take away the covenant of salvation, and there remains no hope. I have translated τῶν διαθηκῶν by the tables, or, in ordinary legal phrase, the instruments. By solemn ritual did God sanction His covenant with Abraham and his posterity, that he would be their God for ever and ever. (Genesis 15:9.) Tables of this covenant were ratified by the hand of Moses, and intrusted, as a peculiar treasure, to the people of Israel, to whom, and not to the Gentiles, “pertain the covenants.” (Romans 9:4.)

Consider also these quotes from Calvin's Sermons on the Acts of the Apostles: Chatpers 1-7 (2008):
 
It is true that the law without Jesus Christ is of no advantage but works for the condemnation of men.  However, if we receive it with the promises it contains, we will at that time find everlasting life because Jesus Christ is encompassed within it, for he is its soul 603)
 
In the first place, our Lord had provided Moses with adequate approval by performing so many mighty acts and miracles by his hand.  With that, Stephen shows that the acusation against him of detracting from Moses' honour and authority was false.  Therefore, he both concludes and confesses that Moses was an outstanding prophet of God and had done great things for the people's redemption.  we can judge from that his intention was not to encourage disobedience to the law of Moses.  But he does want to show that all of the outward ceremonies had come to an end because Jesus Christ, who is their truth, fulfilled them with his coming.  And that is the main thing we must consider here.  The account of this story would be of little value if we did not always have before us what Stephen asserts.  For just as he spoke to the Jews of that period, so also is that teaching recorded for us so that we might know that Jesus Christ did not come to destroy the law but to confirm it (Matt. 5:17).  The gospel then is not a teaching contrary to the law of Moses.  It is rather a more adequate revelation and confirmation of the things shown earlier.  And in that, we see how the whole of holy Scripture is in agreement.  We see how all those whom God instructed from the beginning of the world are in agreement, as if they had spoken with a single voice. 
The quote is taken from Calvin's Sermons on Timoty and Titus:
 

We see what S. Paul’s meaning was in this place, and what we have to mark upon these words: to wit, that to profit well in the law of Moses, we must begin at this end, to wit, to have faith in God: and thereunto also wee see that the law is very profitable for us.  And we must not do as vile hogs, which always have this word in their mouth, or rather in their snouts: “Oh, all is at an end, we have to beat our heads no more about the old Testament.”  We shall see some that are mixed among us, as swine among the sheep and lambs of our Lord Jesus Christ, which will belch out such blasphemies.  But on the contrary side, S. Paul pronounces here, that if we read the law of God diligently, and seek in wisdom of Spirit that which is contained in it, it shall serve us for a good instruction, to brin us to faith, as also we see it be experience: for from whence did our Lord Jesus Christ and his Apostles draw their doctrine, but out of Moses?  And if we well consider all, we shall find that the Gospel is but a simple expounding of that which Moses preached before.  It is true that there was a darkness in the shadows and figures of the law, and that God was not so gracious unto the fathers as to us: yet so it is, that the substance of the Gospel is drawn from thence, and we have the same faith that [pg. 29] they had, which lived before the coming of our Lord Jesus Christ.  Let us therefore at this day profit at the law of GOD, and let us not lose such a treasure, and let us not suffer these villains and shameful creatures to turn us aside from it and rob us of it.  I have already shown how we must learn to be faithful by the law, to wit, by knowing this covenant which God has made with men of his free mercy.  It is true that he chose the stock of Abraham first of all: yet notwithstanding, seeing the goodness which he then showed but to one people, ought to spread itself throughout all the world, we are at this day of that sect of people, and therefore heirs and partakers of the promise of salvation, which was before time given to Abraham.  For when we know that God has chosen us to himself, and will keep us as his own household, we may well claim him as our father, and flee wholly to him: we have not to make any more doubt of his love towards us, and whether GOD love us or no.  And herein lies all our happiness: we lack nothing when we are once assurance of God’s grace: and so the way to learn faith by Moses’s doctrine is to know that GOD did not ordain so may sacrifices, and washings, and such like things in vain.  Let us also know that God gave not his people fools babbles, as they term them: nor that the solemn sacrifices that were used, were toys for little children to play with all: for there was the spiritual pattern that Moses saw in the mountain.  And thus let us mark that our Lord would keep his people to himself by the means of our Lord Jesus Christ: and thereon it is, as I said, that our faith must reast, and wholly lean upon, for if we have not Christ Jesus before our eyes, it is impossible for us to know anything of God (Sermons of M. John Calvin on the Epistles of S. Paule to Timothie and Titus (1579) 29-30).