Reposting this 2013 review because the Kindle Edition is on sale for $3.25
Takeaway: The world is not what it seems.
This is a wide ranging book, originally written as a trilogy in Japanese . It is hard to classify it as a genre, but I would probably call it a contemporary fantasy. Although I think that most of the people that will like it would not pick up a book labeled fantasy as a first choice.
Aomame (the female protagonist) opens the book late for an appointment. She is stuck on a skyway in a cab. The cabbie suggests that if she really needs to get to her appointment she could get out of the cab, climb down an emergency ladder and take the subway (which has a stop near the bottom of the stairway.)
Aomame decides to do this, but the cabbie warns her that nothing will quite be the same once you have stepped outside the realm of your normal life. And nothing is. Aomame is not going to any old business appointment. She is on her way to assassinate a man who beats his wife. She has a relationship with a rich older woman that provides her with information (and money and support) to kill men to stop them from beating their wives.