What is the ruling regarding a man divorcing his wife while he is angry and she is menstruating, then taking her back, then divorcing her again while she is menstruating and he is in a state of extreme anger, then taking her back, then divorating her in writing while she is menstruating and he is in full control of his mental faculties? Is it permissible for him to take her back after all these divorces?

If the wife was divorced three times, and the first and third divorces were effective because they occurred during menstruation, which does not prevent the occurrence of divorce according to the majority of scholars. As for the second divorce, if it occurred during intense anger where you were unaware of what you were saying, then the divorce does not take effect. In this case, the divorce would have occurred twice, and you can take her back before her iddah (waiting period) ends. However, if you were aware of what you were saying at the time of the second divorce, then she is unlawful for you and will not become lawful again unless she marries another man and he divorces her after consummation. It is advisable to consult scholars in your country.