And I, behold, I establish my (h) covenant with you, and with your (i) seed after you;
(h) To assure you that the world will never again be destroyed by a flood.
(i) The children which are not yet born, are comprehended in God's covenant with their fathers.

And I, behold, I establish my covenant with you,.... Not the covenant of grace in Christ, but of the preservation of the creatures in common, a promise that they should not be destroyed any more by a flood; to which promise it seems an oath was annexed, as appears from Isaiah 54:9 which passage refers to this covenant, as Aben Ezra on the place observes; and both to raise attention to what is here affirmed, and to show the certainty of it, the word "behold" is prefixed to it; nor is it amiss what Jarchi observes, that this follows upon the direction and exhortation to procreation of children, and is an encouragement to it; since it is assured that posterity should be no more cut off in the manner it had been; for this covenant was made and established not only with Noah, and his sons, but with all their succeeding offspring, as follows:
and with your seed after you; with all their posterity to the end of the world; so that this covenant was made with all the world, and all the individuals in it, from Noah's time to the end of it; for from him and his sons sprung the whole race of men that peopled the world, and still continue to inhabit it; hence here is nothing in it peculiar to the seed of believers.

We have here the general establishment of God's covenant with this new world, and the extent of that covenant.