Long book. I loved the first part. The 2nd and 3rd parts were OK.
In part 1, the moon blows up. No one knows why. People realize than in a year or two the lunar debris will destroy the earth in a "Hard Rain" There is a mad scramble to send enough people and equipment up into space to keep humanity going.
Part 2.. the Hard rain destroys the Earth. The people in space try to establish them selves as a civilization. Conflict, bolides an other challenges kill off all of humanity until only seven woman are left—the Seven Eves.
Part 3… Its 5000 years later. Humanity has recovered. 3 billion people are living in space stations around the earth. For the past centuries they have been terra forming the earth to make it habitable again.
Some parts of Seveneves probably say more about the author than about his fictional universe. The world of Stephenson Seveneves has a hard break between religion, emotions and technical perspectives. Very explicitly, in Seveneves the human races that are bread for emotions all end up being the bad-guys. Religion and the spiritual is literally killed off. Stephenson doesn't realize that scientists and technocrats have emotions too. That emotions give us energy, focus, purpose. The emotional intelligence and leadership isn't about manipulating people. It's for taking control of our energy, or focus, our purpose. We are not machines.