The Lesser and Greater Divorce in Talaq?

Question : May Allah reward you. This questioner says: Honorable Shaykh, I ask for clarification of the difference between the greater and lesser divorce in talaq?

Answer : A divorced woman may be in a state of raj'i (revocable) divorce, or in a state of ba'in (irrevocable) divorce with a lesser separation, or in a state of ba'in divorce with a greater separation. The one with a greater separation is she who does not become lawful to her husband again except after marrying another husband; she is the one who has been divorced three times. An example is a man who divorces his wife, then she completes her waiting period, then he takes her back with a new contract or by revocation, then he divorces her a second time, then he takes her back, then he divorces her a third time. This third divorce makes the woman ba'in with a greater separation. What does "greater" mean?
It means she is forbidden to him until she marries another husband. As for the ba'in with a lesser separation, she does not become lawful to her husband except with a new contract, even if she has not married another husband. An example is a man who divorces his wife in exchange for compensation, meaning the woman agreed with him that he would divorce her and she would give him ten thousand riyals, for instance. If he divorces her on this basis, she is then ba'in with a lesser separation. It is called ba'in because she does not become lawful except with a new contract, and it is called a lesser separation because she becomes lawful even if she has not married another husband. The third category remains: the raj'i (revocable) divorce. The raj'i is that in which the following conditions are met in the separation: that the separation is by talaq, that it is without compensation, that the wife has been consummated with or sequestered with, and that it is before the completion of the number of divorces the divorcer possesses. How many are these? That the separation is by talaq, that it is without compensation, that the wife has been consummated with or sequestered with, and that it is before the completion of the number. An example is a man who marries a woman and consummates the marriage, then he wants to divorce her for a legal reason, so he divorces her. This is raj'i. He may take her back as long as she is in the waiting period without a marriage contract; rather, he says to two men whom he brings, "Bear witness that I have taken back my wife so-and-so." If he separates from her by annulment rather than by talaq,
such that there is a dispute between them and people of good intervene and annul the contract, then there is no raj'i (revocation) in that. If he annuls her marriage because of a defect in her, there is no raj'i. If he divorces her in exchange for compensation, even if it is small, there is no raj'i. If he divorces her before consummation and seclusion, there is no raj'i. If he divorces her with the last of the three divorces, there is no raj'i. Yes.