The Better Covenant--Founded upon Better Promises

In Hebrews 8:6, it says that Jesus "has obtained a more excellent ministry, inasmuch as He is also the Mediator of a better covenant, which was established on better promises." So, when Jesus was crucified on the cross for us, He did it to establish the New Covenant with us that is in every way superior to the previous one. So, today I would like to look at the differences between the New Covenant and the Old Covenant and see why it is such a better covenant, what the better promises are, and what this means for us now.