The covenant is the relationship of friendship that God makes between Himself and His chosen people in Christ. Far from being a cold, business-like contract or bargain, as some teach, the covenant is a warm, intimate bond of fellowship in which God is our God and Father and we are His people and children. This is the very essence of our religion, walking and talking with our God through Christ and His Spirit, and looking forward to that day when we will do so perfectly and eternally in the new heavens and earth (Genesis 17:7, Jeremiah 31:31-33, Ezekiel 16:8, II Corinthians 6:14-18, Revelation 21:3-4).
There is only one covenant, unfolded and established by God throughout history in different ages known as dispensations each of which reveals a specific aspect of the one covenant: e.g., the covenant with Adam, Noah, Abraham, Israel at Mt. Sinai, and King David. We also read of the old and new covenants referring to the covenant in its old form (the law) and its new form (the gospel). (Galatians 4:22-31, Hebrews 8:6-13)
The covenant is first of all between God and Christ, who is the Seed of Abraham (Galatians 3:16), and then with all believers in Christ (Galatians 3:29), that is, all the elect. God gathers His elect into the covenant from two places: the mission field and the children of believers (Genesis 17:1- 8, Acts 2:39). God generally gathers the children of believers into His covenant. Therefore, we baptize our children because they too are members of the covenant.
The covenant is unconditional in its establishment, maintenance, and final perfection. God unilaterally does all of this. He never says to us, “Come, let us make a covenant together.” But He makes the covenant with us. He does not promise to give the blessings of the covenant to all children of believers, and then tell them that they have a responsibility to fulfill a condition, to do something, to believe in Christ and walk in obedience, in order to receive those blessings, either in this life or in the life to come. But He promises to establish His covenant with all the elect children of believers, and works faith in their hearts, and gives them the blessings freely, without them having to fulfill any condition to receive them (Romans 9:1-13, Galatians 3:6-18). Thus, it is indeed a covenant of grace!