What is the Sharia ruling regarding the relationship between a couple where the wife discovered her husband's repeated infidelity, and she requested a divorce after he had already divorced her twice, but he refuses? And is it permissible for her to remain with him?

Adultery is one of the major sins, but it does not sever the marital relationship nor does it forbid the adulterer to their spouse. The wife has the right to refer her case to the Sharia (definition) judge to remove the harm inflicted upon her due to the husband's persistence in adultery. If there is no judge, Islamic centers in European countries act in his stead. It is not permissible for the wife to independently initiate a divorce, and such a divorce would have no legal effect. If the husband divorces his wife in a legally valid manner, there is no harm in documenting it before secular courts. If the spouses dispute over the divorce, Islamic centers act as the Sharia judiciary. Resorting to secular courts to terminate the marriage legally does not terminate the marriage Islamically. Therefore, if a woman obtains a civil divorce, she should then approach Islamic centers to finalize the matter according to Sharia.