"But Noah found favor in the eyes of the Lord." NIV translation
This is the first case of God keeping a remnant of mankind for Himself. This is a pattern that we will see throughout the Old Testament as well as to the end of this age in Revelation.
"This is the account of Noah. Noah was a righteous man, blameless among the people of his time, and he walked with God." NIV translation
We see that Noah wanted to honor God and so did not do the things that the rest of the people around him were doing. We, as Christians, are God's remnant in this world today but too many people are forgetting the fact that a remnant does not get caught up in doing the same things as the rest of the world. A remnant stands out as being different instead of blending in with the crowd.
"Noah had three sons: Shem, Ham, and Japheth." NIV translation
Here, we see God's will for man displayed again in the fact that Noah had three sons.
"Now the earth was corrupt in God's sight and was full of violence. God saw how corrupt the earth had become, for all of the people on earth had corrupted their ways. So God said to Noah, 'I am going to put an end to all people, for the earth is filled with violence because of them. I am surely going to destroy both them and the earth.'" NIV translation
Now, we see that this mixing of the children of God with those that were not has resulted not in more children of God but in God's people turning their back on Him. God told Noah that judgment was coming for all of them and the same thing is true for us today.
"'So make yourself an ark of cypress wood; make rooms in it and coat it with pitch inside and out. This is how you are to build it: The ark is to be 450 feet long, 75 feet wide and 45 feet high. Make a roof for it and finish the ark to within 18 inches of the top. Put a door in the side of the ark and make lower, middle and upper decks.'" NIV translation
God gives Noah specific instructions on building a large boat so that he may be saved from the coming flood. We see that God did not give him a selection of boat plans to choose from but instead gave him exact plans for the ark. That reminds us of the fact that there is only one way that we might be saved and that is through our ark which is Jesus Christ.