This is important, but I forgot it y'day, ooops1
There were 2 covenants, the covenant of works, which Adam was under & lead to death for us all, as Adam was the Federal representative of the human race. the terms were, 'don't eat that tree, or dying you shall die' is how the Hebrew in Gen 2:17 is. The other, was the covenant of grace which everyoone has been under since Gen 3:15.
Adam blew the terms of the cov. of works, God didn't leave them dead in their sin, He came to them in the cool of the day, offered an opportunity for them to confess their guilt (Gen. 3:11, Gen 3:13), promised Christ, the Seed of the woman who would one day crush the head of Satan (Gen 3:15, 'crush' is a better translation of the Hebrew there than 'bruise') & taught them how to make a blood sacrifice which He provided, covering their sin, Gen. 3:21. All this ushered in the covenant of grace, (quoting A.W. Pink now) "which is an everlasting covenant, Is 55:3, a covenant of peace, Ezek 34:25,37:26. It secures reconciliation with God, for Adam's transgression produced enmity, but by Christ the enmity has been removed, Eph2:16 and therefore He is denominated the "Prince of Peace" Is 9:6. It is ccalled the "covenant of life" Mal 2:15in contrast to the covenant of works which issued in death, because life is the principal thing pledged in it..."etc. When the Bible calls Christ "the last Adam",Ro 5, 1 Co 15, among the many things this refers to, His status as a new Federal Head of His people is referred to. He is the neew covenant, and the mediator of it.
Back to the Garden of Eden.
Adam responds in faith, believing God isn't going to wipe out the entire population at that point in history because of their sin, which he demonstrates by naming his nameless to this point wife Eve, 'the mother of all living.' Gen 3:20
Eve demonstrates her belief in this new covenant of grace/peace/life/ etc. by naming her firstborn Cain, a name which means "I got Him!" wrongly thinking she was the momma of Christ. Little bit mistaken, butcha gotta admire her zeal!
All the subsequent covenants, the Noahic, the Abrahamic, the Davidic further flesh out this central covenant of grace. If you can imagine the covenant of Christ being like the bridge that fills the gap between the unregenerate & God, all the 'little' covenants along the way are like road signs, pointing out the path one should take to get to Christ. They also served to be reminders to God's people where eternal life comes from, which served to help the elect of the OT keep their eyes on the covenant, or Christ. No wonder Mary, during her miraculous pregnancy, praised God for His keeping the covenant, Luke 1:46-55.
Hope that helps!
The covenant is enormously interesting & eternally important, well worth the time to study it deeply. This Pink book I'm reading is called "The Divine Covenants", and it is so excellent! Not one I can whip through, too chock fulla huge ideas with enormous ramifications.