Chapter 6 starts off with a description of what was happening in the world. Verse 2 says that the "sons of God" took wives for themselves from the "daughters of men." The best explanation I have read for this is the most straightforward one...fallen angels were marrying human women and having children with them. This would become possible by them possessing human male bodies. Chapter 6 then goes on to talk about the Nephilim and men of renown. While the term Nephilim comes from a Hebrew verb root that means "to fall". I used to think that the Nephilim were the race of people who were the offspring of "fallen" angels and humans, but the verb implies that these Nephilim were giants that "fell" on people in a sense of overpowering them.
Chapter 6 then goes on to describe how God saw that the thoughts of man's heart was continually evil, and it grieved Him. Thus, He decided to destroy the human race and all animals, birds and creeping things. The only person to find favor with God was Noah, and thus he was given the instructions for building the ark. 120 years later, after building the ark with his 3 sons and preaching to a hardened people, Noah and his family was protected from the flood while the rest of humanity was eradicated.
The kind of faith that it took for Noah to build this ark is incredible. God told him that in 120 years a bunch of water would fall from the sky and kill everyone and everything, so he'd better build a boat that could hold his family and 2 of every living thing (even more of some creatures). I'm not sure how true this is, but I've heard the speculation that it may have never rained on the earth before the Flood. That would make this even more incredible, the fact that Noah had never even seen rain before and yet believed that God would destroy humanity with it. This is the kind of faith that earned Noah a mention in the Hall of Faith in Hebrews 11. And yet, as we'll see in a few minutes, while he was a man of great faith, there was nothing super about him, and he still made his mistakes.
The floodwaters receded, and God made his covenant to never destroy humanity by flood again. He put the rainbow in the sky as a sign of this covenant. What happened afterward is interesting to me. So now there are 4 men and their wives left alive, and it's their job to repopulate the earth. So all of the tribes and peoples of the world descended from one of Noah's 3 sons (as far as I know, Noah did not have any more children after the flood). The lineage of Israel and therefore Jesus Christ came through Shem. The other lineage that is of special notice in this situation is that of Ham.
Verse 20 of chapter 9 picks up an interesting story. Noah began farming and planted a vineyard. He became drunk from the wine and was naked inside his tent. Ham saw this and went and told his brothers about it. Instead of looking at their father naked, Shem and Japheth took a garment and walked backwards into the tent with it on their shoulders and covered Noah with it. When Noah "awoke from his wine" (I honestly have no idea if this means he literally woke up or if he just sobered up), he knew what Ham had done. I would think that the better explanation is that he was never actually asleep during the whole event, and thus he knew how each of his sons responded to his nakedness. For reasons not disclosed, he was unhappy with the way Ham responded and cursed Ham's son, Caanan. He declared that Caanan would be a servant to Shem. It's important to note here (and I never realized this until now) that this is a foretelling of the Israelites conquering the Caananites and taking their land. I learned that the term "servant" could simply apply to a conquered people, whether they became actual household servants of the conquering tribe or not. Therefore, this is an early proclamation of promise that the Israelites would reside in Caanan, long before the covenant was made with Abraham.