The first thing Noah does on dry ground is build an altar — before he rebuilds a house, before he plants anything, before he does a single practical thing to secure his family's future, he worships. And God "smelled a sweet savour," and says in His heart He will not curse the ground again "for man's sake," even though, in the very same sentence, He repeats almost word for word the diagnosis of human corruption from chapter six. That's worth sitting with: the verdict on humanity hasn't changed at all. What's changed is God's committed response to that unchanged verdict. Grace isn't given here because humanity improved. It's given in spite of the fact that it plainly hasn't.
Then the covenant — and its shape is different from every covenant that comes after it. It's unilateral: no conditions laid on humanity in return, unlike the covenant at Sinai centuries later. And it's cosmic in scope, extended explicitly to "every living creature," not just to Noah's family. The sign is the bow in the clouds — and the Hebrew word, qesheth, is the ordinary word for a warrior's weapon. God hangs up His own bow, and hangs it pointing toward heaven, away from the earth — a sign aimed, in some sense, at Himself as much as at us, a self-binding promise never to do this again. Isaiah will pick this up centuries later, in chapter fifty-four, calling it "the waters of Noah" and using God's oath then as the very ground of His promised covenant of peace to Israel — if God kept that oath, His people can trust the next one.
There's a second layer given here too, easy to skip past: the permission to eat meat (9:3), and the command against murder grounded specifically in the image of God — "whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man." This is the first time capital justice is grounded explicitly in the imago Dei rather than simply commanded. And centuries later, when the Jerusalem council in Acts fifteen has to decide what to require of Gentile believers entering the church, they reach back — almost certainly — to exactly this cluster of Noahic commands: abstaining from blood, from things strangled. Paul's Gentile churches are being asked to keep something like the covenant God made with all humanity through Noah, not the covenant made later and specifically with Israel through Moses. That's a detail worth holding onto if you ever wonder how the earliest church decided what applied to everyone and what didn't.