In the preceding passages we see how a covenant between two men was made. Now we turn to the covenants that God has made with man. There are four key covenants in the Old Testament where God makes a covenant with Man.
In Genesis 3, after man has been put out of the garden, God establishes the consequences of their sin. At the same time he makes provision for a redeemer. Notice the phrase "He shall bruise his head". In the New Testament this is clarified to mean Jesus will overcome Satan and sin. This covenant is often referred to as the Adamic Covenant. Note that only God is bound by that covenant. He is responsible to bring it to pass. Note that God has always been in covenant with man and has always made provision for him. The promise of a redeemer has been there from the beginning.
In Genesis 9 the end of the story of Noah results in a covenant God made with Noah and all future men. He would never again destroy the earth and its inhabitants with flood. In this covenant God introduces the fact that man is not to eat flesh with its life. With Adam they had all of the earths produce as food.
The next covenant is with Abraham, called the Abrahamic or Patriarchal covenant. Patriarchal is used to reference the fact that God restates His covenant with Isaac and Jacob. Here God establishes the full covenant he has with man.
In 2 Samuel 7:11 and Psalms 89:3,4 is the Davidic Covenant. It is a covenant God establishes with David that the Messiah would come from his lineage.
In all four of these covenants, God Himself takes full responsibility to fulfill the covenant. He does not state his method or timing. But His promise in each covenant is sure.