Short answer
Yes, and some of it is obligatory. Every woman must learn the basics of belief, prayer, purity, fasting and halal and haram, exactly as a man must. Further study, religious or worldly, is praiseworthy, and Muslim communities need women doctors, teachers and scholars. The limits are the usual ones of hijab and avoiding khalwah.
Knowledge of one's own obligations is fard on every woman. Useful worldly study is permitted and can be rewarded, and some fields, such as medicine for women, are a communal need. Many Hanafi muftis prefer women's institutions and allow mixed ones when there is need and the limits of hijab, gaze and khalwah are kept.
The four schools agree on this.
Explanation
The first word of the Quran to be revealed was "Recite". Allah asks whether those who know are equal to those who do not, and teaches the dua: my Lord, increase me in knowledge. None of this is addressed to men only. The Prophet ﷺ promised a double reward to a man who educated a slave girl well and then freed and married her, so even the most powerless woman of that society was meant to be taught.
The women of Madinah took this seriously. They asked the Prophet ﷺ for a day of their own for lessons, and he gave it to them. Aishah became one of the great teachers of the Ummah. See can women be Islamic scholars.
What scholars say about modern education:
- Fard knowledge first: a girl should not graduate in chemistry without knowing how to pray, how to make ghusl, or the rules of her period.
- Worldly study is good when it is useful and does not take her into haram. Women doctors, nurses and teachers serve the community in ways men cannot.
- Mixed campuses: allowed with need, hijab, lowered gaze and no khalwah. Women-only options are better where available. See free mixing.
- Studying abroad: long travel has its own rules; see travelling without a mahram.
Stopping girls from learning has no basis in the Sunnah. For more, see Quran verses about education and hadith about seeking knowledge.
The evidence
Quran, Surah Az-Zumar 39:9
أَمَّنْ هُوَ قَٰنِتٌ ءَانَآءَ ٱلَّيْلِ سَاجِدًۭا وَقَآئِمًۭا يَحْذَرُ ٱلْءَاخِرَةَ وَيَرْجُوا۟ رَحْمَةَ رَبِّهِۦ ۗ قُلْ هَلْ يَسْتَوِى ٱلَّذِينَ يَعْلَمُونَ وَٱلَّذِينَ لَا يَعْلَمُونَ ۗ إِنَّمَا يَتَذَكَّرُ أُو۟لُوا۟ ٱلْأَلْبَٰبِ ﴿٩﴾
Is one who is devoutly obedient during periods of the night, prostrating and standing [in prayer], fearing the Hereafter and hoping for the mercy of his Lord, [like one who does not]? Say, "Are those who know equal to those who do not know?" Only they will remember [who are] people of understanding.
Raises the status of knowledge for every believer.
Quran, Surah Taa-Haa 20:114
فَتَعَٰلَى ٱللَّهُ ٱلْمَلِكُ ٱلْحَقُّ ۗ وَلَا تَعْجَلْ بِٱلْقُرْءَانِ مِن قَبْلِ أَن يُقْضَىٰٓ إِلَيْكَ وَحْيُهُۥ ۖ وَقُل رَّبِّ زِدْنِى عِلْمًۭا ﴿١١٤﴾
So high [above all] is Allah, the Sovereign, the Truth. And, [O Muhammad], do not hasten with [recitation of] the Qur'an before its revelation is completed to you, and say, "My Lord, increase me in knowledge."
Teaches the believer to ask for more knowledge.
Sahih al-Bukhari 97
Sahih... وعلمها فأحسن تعليمها ...
"And he taught her and taught her well."
The Prophet ﷺ promised a double reward for educating a slave girl, so educating women is rewarded.
Where the ruling is recorded
- Radd al-Muhtar (Ibn Abidin), Introduction, on the knowledge that is fard on every Muslim. Knowledge needed for one's own worship and dealings is fard on men and women.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.