Is it permissible for an adulterer to marry the woman with whom he committed adultery, and what is the Shar'i ruling on their marriage?

It is not permissible for a fornicator to marry the woman with whom he committed fornication unless she repents and undergoes a waiting period (istibra’) of one menstrual cycle if she is not pregnant, or by giving birth if she is pregnant. This is to ensure that the water of fornication does not mix with the water of marriage, and so that the child is not wrongfully attributed to the fornicator if she conceives from the fornication. There is another opinion that states istibra’ is not obligatory if the fornicator wishes to marry her.