What is the significance of “with thee will I establish my covenant” (Gen 6:18)?

This is the first instance of this important word’s occurrence in the entire Bible. While one might say that God had a covenant with Adam and Eve—do not eat of that one tree, and you can continue to live in the Garden—it is not named by God as a covenant, which is a thing God does do later. But what is the covenant God refers to? Consider that, immediately after declaring that he would make a covenant, he says “thou shalt come into the ark.” So, is ordering Noah into the ark, or even promising to save Noah, the covenant? No. The word’s proper context is given by the previous verse: God just got done saying “every thing that is in the earth shall die,” except you, Noah, and why? Because it is with you that I will establish my covenant after the Flood. And indeed God does so when Moses sacrifices to God in gratitude, and God in turn sets the covenant rainbow in the sky, signifying the “common grace” under which all humanity would live (Gen 9:8-17), which seems to be closely associated the preceding, brief Noachian code of law (of Gen 9:1-7). For more, see questions on Gen 9.