Through whom would the seed of the woman come?

The seed of the woman would come through Abraham and his offspring, for the Abrahamic covenant builds on God's promise of a Redeemer through the woman. That promised seed is Christ, who would bruise Satan's head at the cross, though Satan would bruise His heel.

Les explains that in Genesis 3:15 God addresses Satan and puts enmity between Satan and the woman, and between Satan's seed and her seed. That seed of the woman, Les identifies, is Christ. There would be a running battle between Satan and Christ: the seed of the woman would bruise Satan's head, which happened at the cross, while Satan would bruise His heel, accomplished when he caused Christ's suffering at Calvary. Les then shows that from this promise of a Redeemer through the woman, the Abrahamic covenant is built, teaching that it would be through Abraham and his offspring that the seed of the woman would come.

Genesis 3:15

And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.

What did God promise Adam in Genesis about the seed of the woman?

In Genesis, God promised Adam that the seed of the woman would one day defeat sin and death and Satan. That promise was later expanded when Abraham was told this same seed would come through his lineage and the nation of Israel, pointing ultimately to Christ.