Genesis was written by Moses many years after the events of the book took place. Jesus himself confirmed that Moses wrote the book when he said "If you believed Moses, you would believe me; for he wrote about me." (John 5:46)
The heartbeat of Genesis is the sinful state of man and his need for a Savior. God created man so that He could have intimate communion and fellowship with him. But the entrance of sin in the Garden of Eden broke that relationship between creation and the Creator. Although Adam and Eve had to pay a painful price, their excommunication from the garden came with a promise: one day Satan will be defeated, and the relationship between God and man will be restored.
In the book of Genesis, Jesus Christ is that promise, the Promised Seed. Everything that takes place in Genesis is simply preparations for that promise to be fulfilled. From the Flood, to the Tower of Babel, God was working to keep the bloodline pure, so that one day a man named Abram could be called out of the land of Ur to become the father of many nations, and the chosen people of God. Then God changed his name to Abraham, sealing the covenant and setting in motion His plan for redemption. (Genesis 17:5)
The promises that God made to Abraham were fulfilled in Jesus Christ, many centuries later. Because of Jesus' crucifixion and resurrection, the nations of the earth were reconciled to God, the very promise that God had spoken to Abraham. But the story doesn't unfold without the twists and turns of man's mistakes and the interventions of God.
Abraham's son, Isaac, born to him in his old age, grew to be the father of Jacob, who was chosen by God to become the father of 12 sons. The descendants of these sons eventually became the twelve tribes of Israel, God's chosen people. But before they became a nation, eleven of these sons, along with their father, Jacob, moved to Egypt to escape a famine that was threatening much of the land. It was there in Egypt that Jacob and his eleven sons were reunited with Joseph, the twelfth son whom the other brothers had spitefully sold to traveling merchants many years before, in an attempt to appease their jealousy of him. Joseph, without a trace of bitterness, embraced his long-estranged brothers, and welcomed them into Egypt, providing for their needs and ensuring their safety and survival.
This is where Genesis ends, with Joseph's expectation that one day God would bring them out of Egypt and back to the land that He had promised to Abraham many years before. He was so certain they would one day return that he instructed that his bones be carried out with them when they leave Egypt. Joseph knew the covenant God had made with Abraham, and died with the expectation that God would do what He said He would do. That same hope echoes in the expectation of the coming Messiah that was promised many generations before. But before the Christ could come, more preparation needed to take place. That is where the next stage begins, in the book of Exodus.