One who divorces his wife, and after that she engages in nonmarital relations with another, she is permitted to return to her husband. Ram''a: And this is also the case if she engaged in nonmarital relations with the first [husband], then she was betrothed to a second [husband], who divorces her, she is permitted to return to the first [husband], even if she was designated to him first. Shulchan Arukh: But if she was betrothed to another and he divorced her, or he died, it is forbidden for her to return to the first [husband]. Ram''a: And even if she was only divorced on the basis of mere gossip.
A deaf person who divorces by hinting and she went and betroths a different deaf person, and it goes without saying to a hearing-person, she is forbidden to return to her deaf husband. But the wife of a hearing-person that was divorced, and she went and married a deaf person, and was divorced, she is permitted to return to her hearing-husband.
One who sends out his wife because of a bad reputation about her, or because she is a person who habitually vows, or because she is barren, he may not accept her back. And there are those who say, only if he said to her: Because of this [reason] I am sending you out, and doubles his words to say, were it not for this, I would not be sending you out. But if he did not double his words, he is able to accept her back. And there are those who say that if he said to her: Because of this I am sending you out, even though he did not double his words, he is not able to accept her back. And there is one who says, that even if he did not say to her: Because of this I am sending you out, he may not accept her back.
One who sends out his wife because she saw blood every time she had sex, he may not accept her back.
All of these that said, he may not accept her back, if he sinned and accepted her back before she was betrothed to another, he should not send her out; and if he sent her out, if he had sons from when she returned, it is permitted for him to accept her back, in order to not subject them to scorn.
One who sends out his wife because of one of these things, they say to him, know that you will not be able to ever accept her back.
One who sends out his wife because of a vow that he vowed to send her out, he is able to accept her back.