Covenant Theology is the Reformed way to read the Bible. The Bible is all about Christ, and therefore it’s also about His people, who are united to Him through the Covenant. This is why marriage is a Covenant, to illustrate the bond between Christ and His Church. Because the whole Bible is about the Church, meaning, God’s people, we must assert the continuity of the one overarching Covenant of Grace that unites us to Christ. The Church has existed since Adam, as stated in our Scots Confession, and has been governed by the many Covenants, which are all part of the Covenant of Grace. There are other parallel Covenants, but they are theological constructs in order to explain God’s workings. All the Covenants that are actually labeled as such are part of the Covenant of Grace.
The Covenants build on each other, and are all fulfilled in Christ. The first administration of the Covenant of Grace is with Adam, where God promises the defeat of Satan, often called the proto-gospel. The next administration is the Noahic Covenant, where God promises to show grace to the world and the creation collectively. In adding this promise, the previous one is in no way removed. With the Abrahamic Covenant, God actually creates a visible Covenant people, despite having already had an “elect” people. With the Mosaic Covenant, God gives the Law and sets apart His people as holy and gives them a system for communion with God. With the Davidic Covenant, God gives the promise of a Kingdom that will have no end.
All of this is fulfilled by Christ. Salvation has always been the same process – by trusting in God’s Covenant promises, but more is revealed over time. Everything given in the Covenants still stands, just in different forms. We still have what we had under the Mosaic sacrificial system, because as Hebrews tells us, it was never the sacrifices themselves that saved us, but rather they pointed to the sacrifice Christ gave us, and now that that’s been revealed to us, we have no more use for earthly sacrifices.
Parallel to the Covenant of Grace is the Covenant of Works, which God made with Adam when telling him not to sin, lest he die. The Covenant of Works shows why the Covenant of Grace is necessary, because we need to be redeemed from sin. The Covenant of Works was made with all of humanity, whereas the Covenant of Grace, starting with Abraham, was only made with the Church (The Covenants with Noah and Adam do indeed apply to all humanity). The deal was that humanity would live if we obeyed, and die if we didn’t, and we didn’t so we deserve to die.
The deepest underlying Covenant is the Covenant of Redemption. Christ is the hero of the Biblical story. The Father gives a bride (the elect) to the Son, which He needs to undergo the worst of trials to win. And the Holy Spirit is the one who proceeds from the Father and the Son in order to unite the elect to Christ, and therefore, to the Father. The Covenant of Redemption is an agreement from before time about the plan of salvation. The Father would elect some people, the Son would die for them, and the Holy Spirit would apply salvation to them and unite them to the Son. This is why Limited Atonement and Calvinistic double-predestination flows logically from Covenant Theology.