Islam has opened the doors of education for both men and women. They will be adorned with education since childhood itself. If a girl could not be educated and she gets married and now she takes the permission of her husband for education, then should the husband give her permission or not? Education is the life breath of Islam and the pillar of the religion. It is compulsory for every Muslim men and women to acquire the basic knowledge of Islam, as the Holy Prophet (Sallallahu alaihi wa sallam) said: Acquiring knowledge is compulsory on every Muslim man and woman. (Mishkaat, Pg. No. 34)
Here education means to learn the basic tenets about the oneness of Almighty Allah and the Prophethood and the necessary rules of Taharah (cleanliness), Salaat, fasting, etc. Learning these is necessary for every Muslim, as given in Mirqaat Sharh Mishkaat, Vol. 1, Pg. No. 284.
If the woman does not know these and asks permission of the husband to acquire this knowledge, then either the husband should teach her these himself or arrange for her education. In the latter case, it is better to permit the lady to step out of her house with complete Islamic Hijab. As given in Radd Ul Muhtaar, Vol. 2, Pg. No. 722.
If the lady is aware of these necessary tenets and issues and she desires to acquire more education and develop perfection then the husband may permit or not. As given in Durre Mukhtaar, Vol. 2, Pg. No. 722.