The Devotion of Suspect X is a Japanese mystery novel, the first in Higashino's Detective Galileo series (at least in terms of English language releases). I bought my copy of this volume brand new.
Review:
Yasuko is a single mother who works in a lunch shop. She used to work at a hostess club but has since left that life behind - along with her abusive ex-husband, Togashi. Unfortunately, Togashi manages to track her down once again, and this time things escalate to the point that Yasuko strangles him to death in an effort to protect herself and Misato, her teen daughter. Yasuko is still grappling with what she's done when her next door neighbor, a math teacher named Ishigami, stops by and calmly offers to help.
Ishigami is a quiet and solitary man whose only interest in life is mathematics...and Yasuko. He had gotten into the habit of stopping by her workplace to buy lunch, just to see her. He has no illusions that she might ever feel the same about him. When he hears the commotion in her apartment, he immediately offers to help. He isn't shocked by what's happened - his only concern is the problem presented by Togashi's death, and Yasuko and Misato's safety. He'll do anything to help them, so he takes care of literally everything, disposing of Togashi's body and laying out exactly what Yasuko and Misato must do in order to deal the police's inevitable suspicion.
The one thing Ishigami doesn't take into account is that the police will involve Yukawa, a physicist who's the only person he's ever met whose intellect is a match for his own.