All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is confirmed in Saheeh Al-Bukhari and Saheeh Muslim that Usaamah Ibn Zayd narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: ''I have not left after me any temptation which is more harmful to men than that of women." Furthermore, Abu Sa’eed Al-Khudri narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: ''Beware of this worldly life and beware of women, as the first temptation for the children of Israel was concerning women." [Muslim]
The above two Ahaadeeth clarify that one has to be very careful regarding the matter of men dealing with women. Being lenient in such matters always leads to trials and much evil, especially since the devil is the enemy of man and he is always lying in wait for him, and he drags him to temptation step by step. It is for this reason that Allaah Says (what means): {O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan — indeed, he enjoins immorality and wrongdoing. And if not for the favor of Allaah upon you and His mercy, not one of you would have been pure, ever, but Allaah purifies whom He wills, and Allaah is Hearing and Knowing.} [Quran 24:21]
Indeed, the reality proves this. For this reason, you should avoid this as it is a means to evil and the Sharee’ah came to block the means to evil; so every means that leads to what is forbidden is forbidden.
A Muslim should not be deceived into thinking that he is steadfast on acts of obedience; as the devil is keener on misleading him as a righteous person than misleading other people who are not righteous. Also, the righteous Muslim should be keen on avoiding places of suspicion.
Indeed, we have already issued Fatwa 82431 clarifying the ruling of studying in an environment where there is forbidden mixing between men and women and that it is forbidden except in case of dire necessity, so please refer to it.
Finally, if we presume that this woman is in dire need of such studies, then she herself has to look for a solution to avoid danger and harm. As far as you are concerned, you should avoid her totally and avoid establishing any relationship with her if you wish to keep your religion and honor blameless.
Allaah Knows best.