And when you divorce the women and they reach (the completion of) their waiting period, then do not prevent them from remarrying (their former or latter) husbands when they have mutually agreed according to the Islamic Law. This is a direction for him among you who believes in Allah and the Last Day. It is most pure, clean and wholesome for you. And Allah knows and you do not know (so many things). Surah Baqarah (2:229-232)
The summary of these verses is that in verse 229 of the Holy Quran, Allah Ta'ala says about Talaq Raj‘ee (The revocable divorce) that after the first and second Talaq, the husband may reconcile with the wife within the Iddah and should fulfil her rights as given. The husband may also let the time period pass and separate from her amiably. After the Iddah, there can be no reconciliation. However, if both of them agree on this, they can marry again.
In the same verse the rules of Khula (annulment of marriage) have been given. The husband cannot take back the Mehr (alimony) and other jewelry given to the wife at the time of divorce. However, if there is a situation that the husband does not want to give divorce and the differences between the couple are such that they cannot live together anymore and the wife is ready to give some money to get her freedom, then in this case, the husband may accept money to divorce her. This is called as Khula annulment of marriage).
In verse number 230, Allah Ta'ala says about Talaq Mughallaza (the final divorce) that after this the husband and wife will be separated. After this, there can be no reconciliation. If after this, they want to marry, then there is only one solution. After the Iddah, the lady should marry somebody else, the marriage should be consummated. Then the husband should divorce the wife out of his own free wish. Then again, the lady should spend the Iddah and only then can she marry the previous husband.
In verse 231, the rules of Talaq Raj‘ee are further explained. The husband can reconcile with the wife only if his intention (Niyyah) is clear, he intends to fulfil all the rights of the wife. If on the other hand, his intention is to trouble or oppress the lady, then reconciliation becomes impermissible.
In verse 232, if the husband does not reconcile with the wife after the first or second divorce and after this the husband and wife want to marry again, then you should not stop them from doing so, neither should you force them otherwise nor should you be angry at this.