This is the kind of book I stay up all night reading. 
 The moon explodes--and scientists are able to conclude that this spells disaster for the earth. Immediately governments and individuals start creating survival plans to outlive the expected 5,000-10,000-year meteorite storm that will "sterilize" the face of the earth. The plot follows those who are launched into space, a small population which is whittled down even further when the inevitable disasters occur. Some characters have thinly-disguised real-life analogues (Neil Degrasse Tyson in particular), which makes the book even more fun. In the end, 7 fertile women--one of whom is a genetic engineering genius--remain to populate future generations as the Seven Eves of the palindromic title. 
 But "the end" is not the end of the book, oh no...there is a last part (or possibly better considered an extended epilogue) that provides a peek at life 5,000 years later and it is wild. 
 A bit of warning--there is a lot of infodump and technobabble in this book. If you're interested in orbital mechanics and cool futuristic space gear, you will love this. If you aren't, these parts can be skimmed for the important bits without spoiling the story. There is also an immense amount of suspension of disbelief involved at points, but I like crazypants SF/space opera as long as it doesn't get to the point of absolute ridiculousness, and this doesn't. I highly recommend this book.