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God's character is seen in the Book of Genesis in a variety of ways. For example, early on in the Book of Genesis, His truthfulness is displayed. When Adam and Eve are put in the Garden to rule and have dominion over it, He gives them a command not to eat from the tree of the knowledge of good and evil. We read the story, we know that Adam and Eve were tempted to eat from it and they did. God had promised that if they did eat from that tree that they would surely die, and we know from the Book of Genesis that later on Adam and Eve did die. So, God gives His word, and He is true to His word.
We also see a picture of God's purity and holiness brought forth from the Book of Genesis. God is against sin. In the Book of Genesis, we read about a spiraling out of control of man's sinfulness and wickedness in the world to the degree that God purposes to bring about judgment, and this will be a global judgment when he brings a great flood on the earth. And so in that flood, he wipes out all of humanity with the exception of Noah's family and the other animal life that's preserved in the ark. So we get a display of God's holiness towards sin in that story.
Now in both those stories, we also get a sampling of God's mercy. We see that when Adam and Eve have sinned and they become aware of their nakedness, God does not completely abandon them, but He provides covering for them, so He shows them mercy in this respect. And also in the flood story, while God is angry with sin while he purposes to bring His wrath upon humanity, at the same time He demonstrates His mercy and His grace in sparing the family of Noah to preserve the human race and to preserve life on the earth.
One last example of God's character in Genesis would be His goodness, and this is seen at the outset of Genesis when God creates all of life. He creates the heavens and the earth, and on this earth, he creates animal life, plant life. And at the pinnacle of this creation, He creates man and woman. He creates Adam and Eve, and to Adam and Eve, He gives the stewardship of all of the creation. So, He's created this beautiful earth He's created all of His life, and to man and woman, He gives this privilege, this honor to rule, to subdue, to have dominion over all the life that is present there. And this is an example of His goodness towards us.