Question:

Is it permissible to teach girls how to read and write?

Answer:

It is permissible once the laws of hijab are practiced. In these times the importance has increased since the knowledge of Deen is only present in books.

The Messenger (صلى الله عليه وسلم) had delegated a woman to teach Hazrat Hafsah (رضي الله عنها) the skill of writing. [Abu Dawud]

However, in all conditions, it is compulsory to completely refrain from mixed-gender education, leaving out hijab and all other vices that people wrongly consider part of education.

(Hazrat Mufti) Muhammad Rafee Usmani (May Allah preserve him)
Nawaadirul Fiqh Vol.2 Pg.382