Is head covering for women an obligation in Islam, and what is the legitimate proof for that, or is it a Sunnah or a tradition, especially since there is no clear mention in the Quran of the obligation to cover the head, as in the verse from Surat Al-Ahzab which commanded wearing the jilbab, not the hijab?

The covering of a woman's head in front of non-mahram men is a matter of scholarly consensus. The evidence for this from the Quran is:

1. Allah's saying: "O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful." (Al-Ahzab: 59).

2. The prohibition for women from displaying their adornment to non-mahrams in Allah's saying: "And let them not expose their adornment except that which [necessarily] appears thereof and let them cast their headcovers over their bosoms and not expose their adornment except to their husbands or their fathers..." (An-Nur: 31).

And from the Sunnah is what was narrated by Aisha that Asma bint Abi Bakr entered upon the Messenger of Allah, peace and blessings be upon him, wearing thin clothes. He said: "What is this, O Asma? Indeed, when a woman reaches the age of menstruation, it is not proper for anything to be seen of her except this and this," and he pointed to his face and his hands (the Hadith is mursal).

The difference of opinion among scholars is regarding the permissibility of uncovering the face and hands, but there is no disagreement on the obligation to cover the head.