If before marriage the man agrees to let the wife study in university, would he be responsible

Wa alaikum salaam wa rahmatullah,

No, the permission would be to the extent of him forgoing his rights which may occur due to her attending university. It does not imply he will also bear the costs of her studies.

This is the legal ruling. However, there is no harm in him paying these expenses when in a financial position to do so. In fact, this would give her the impression that he considers her expenses as his own, thus developing mutual understanding and strengthening the marriage spiritually.

And Allah knows best.

Yusuf Mullan