Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.   Wa alaikum assalam wa rahmatullahi wa barakatuh.   To proceed:     It has been transmitted from the Prophet (peace be upon him) in the two Saheehs from the hadeeth of Aboo Hurayrah that the Prophet (peace be upon him) said, “It is not lawful for a woman to observe an optional fast without the permission of her husband when he is at home.” This means that she should not fast without his permission; und undoubtedly this is for optional fasts. As for compulsory fast, when the time is running out- meaning that if there is little time remaining before the beginning of Ramadaan, then according to the majority of the scholars, it is compulsory for her to fast  before the start of the next Ramadaan- in this case it will be allowed for her to fast even if the husband did not permit her. However, if there is still ample time, she should ask for his permission, because he may need her, and she will say, “I am fasting”, and he would not have permitted her to fast, and he will cause her to break her fast, and cause her discomfiture. Therefore, she should seek his permission.     In short: When the time is constricted, it is not compulsory for her to seek permission, however, it is part of kind treatment of one’s spouse for her to tell him that she will fast. This is as far as compulsory fasts are concerned. As for voluntary fasts, when there is ample time, she should seek his permission , because of the hadeeth of Aboo Hurayrah which states “It is not lawful for a woman to observe an optional fast without the permission of her husband when he is at home,” if she does not know if he will permit her to fast.  In instances where the man is married to more than one wife, and what is apparent is that on the day that the husband does not come to her, he is not considered to be present, because the Prophet (peace be upon him) went to Juwayriyah and he asked her. She said, “I am fasting”. Then he said, “Did you fast yesterday?” She said, “No”. He said, “Will you fast tomorrow”. She said, “No”. He said, “Break your fast”.  What is apparent is that she did not seek his permission because he asked her about the previous days’ fast and the following days’ fast.  So apparently she did not seek his permission. Maybe he was not present, that is, it was not her turn to be with the Prophet (peace be upon him). This is the inference. It can be said that if  the woman knows that her husband will not oppose her fasting and has given her general permission to fast, and he can bear her fast, then she does not need his permission.  However, seeking permission is safer and better.