Covenants in Genesis Part 3

This is my last post on the covenants in Genesis.

I've found Michael Lawrence's comments on the covenants helpful, so below are a few paragraphs from his book Biblical Theology:

Covenant of Creation
This is the initial covenant made with Adam in Genesis 2:15-17. As Romans 5 makes clear, he entered into that covenant as the representative of the entire human race. Its blessings or curses would fall on us all. The blessing was implied - the promise of eternal sinless life. The curse was death. The stipulation was to refrain from eating from the Tree of the Knowledge of Good and Evil, as well as working and guarding the garden of Eden. In Genesis 3, Adam and Eve's loyalty to God was tested. They failed the test and broke the stipulations. The curses followed immediately and have continued to work themselves out through all of history and each of our lives.

Covenant of Redemption
This is an intra-Trinitarian covenant in which the Father, Son, and Holy Spirit agree together to accomplish the redemption of a people. This covenant is implied in Genesis 3:15, and referred to in other Old and New Testament passages (cf. Isaiah 49, Psalm 2, Psalm 110, John 5, Revelation 5). What's interesting about Genesis 3:15 and what suggests that there is covenant behind these words is that in the midst of the curse on the serpent, God himself undertakes obligations and makes promises. This covenant becomes the basis for the covenant of grace in all its various administrations. Its outlines are worked out through the rest of Scripture.

Noahic Covenant
This covenant is made with Noah and all living creatures in Genesis 9:8-17. It's called a covenant of grace because of the unilateral promise on God's part. It's called a covenant of common grace because it applies to all people, whether they trust in God or not. The purpose of this covenant is to provide the field upon which the story of redemption will run its course. Judgment is postponed until redemption is full accomplished. Thus, quite appropriately, the sign of this covenant is the rainbow, a symbol of God the warrior's bow, held at rest!

Abrahamic Covenant
This covenant is recorded in Genesis 15:1-21 and picks up God's original purpose with Adam - the creation of a people who will display his glory as vice-regent image-bearers on earth. However, it's made not with all humanity, but with Abraham and his seed. God does make demands upon Abraham's obedience, but this is fundamentally a covenant of grace. God promises Abraham a people and a place under God's benevolent rule, and the blessings of this covenant will eventually flow to all the earth. The sign of the covenant - circumcision - is given in Genesis 17.

Lawrence, Michael  Biblical Theology in the Life of the Church, A Guide for Ministry (Wheaton: Crossway, 2010), 59-60.