This is the written account of Adam's line. When God created man, he made him in the likeness of God. … When Adam had lived 130 years, he had a son in his own likeness, in his own image; and he named him Seth (5:1-3).

The second point in the meaning of "in the likeness (Demuth)" and "in his image (tselem)" is that man was created as God's son resembling him in his divine nature. In a sense, Adam was given spiritual DNA from God, which was also handed down to the generations after him. It should be noted, however, that as for the heirs of the world after the Fall of Man, only one child—usually the firstborn son—in each generation was chosen as an heir.

After Seth was born, Adam lived 800 years and had other sons and daughters. Altogether, Adam lived 930 years, and then he died (vv. 4-5).

Note the expression, "… had sons and daughters." While many other sons and daughters were born of Adam, Seth is recorded as an heir in the genealogy. However, from chapter 4, we know that Adam had two more sons, Cain and Abel, before Seth. Originally, Cain was the firstborn son who was to be the heir, but Abel was chosen for the following reason:

In the course of time Cain brought some of the fruits of the soil as an offering to the Lord. But Abel brought fat portions from some of the firstborn of his flock. The Lord looked with favor on Abel and his offering, but on Cain and his offering he did not look with favor. So Cain was very angry, and his face was downcast (4:3-5).

The reason why Cain's offering was not accepted was because he did not do what was right following the instruction given to him as he brought the offering to the Lord. So the inheritance was removed from him and given to his brother Abel whose offering was accepted because he did what was right. As Cain watched Abel being blessed as an heir, he became so jealous of him that he ended up killing him. Jealousy is the worst kind of sin, and Jesus was also killed because of jealousy. God declared:

Now you are under a curse and driven from the ground, which opened its mouth to receive your brother's blood from your hand. When you work the ground, it will no longer yield its crops for you. You will be a restless wanderer on the earth (vv. 11-12).

Here the last sentence indicates that Cain was no longer an heir. So, God, out of his mercy, gave him a sign so that nobody would inflict vengeance on him.

In this way, the inheritance was removed from Cain, and given to Abel, but since Abel was killed, it was given to Seth, another son of Adam and Eve. After Seth, it was given to Enosh, and after Enosh, it was given to Kenan, and then to Mahalalrel, and so on. And finally, after Lamech, it was given to Noah. What you need to keep in mind is that the lifespan of these people in this genealogy was somewhere between 700 and 1000 years except that of Enoch, which was only 365 years. The first death, which was the death of Adam, occurred after Methuselah (the 8th generation) was born. If sin had not come into the world, death would not have occurred. And if death had not occurred, the passing on of the inheritance as seen in this genealogy would not have been necessary. The genealogy of God's heirs continues and comes to the generations of Abraham, Isaac, and Jacob. After Jacob the inheritance was extended to all his sons. In the same way, the inheritance given through Christ is extended to all believers.

Therefore, the promise (to be heir of the world) comes by faith, so that it may be by grace and may be guaranteed to all Abraham's offspring--not only to those who are of the law but also to those who are of the faith of Abraham. He is the father of us all (Rom 4:16).