Can Women Travel to Seek Knowledge without a Mahram?
Question

What is the Islamic ruling on a woman travelling to seek knowledge without a Mahram?.
Praise be to Allah.The authentic evidence indicates that a woman is not allowed to travel except with a Mahram . This is part of the perfection and greatness of Islam, which protects honour, and takes care of women and holds them in high esteem, and strives to protect them and guard them against the causes of temptation and deviation, whether she is the one who is tempted or is the source of temptation. 
The evidence includes the Hadith narrated by Al-Bukhari (1729) and Muslim (2391) from Ibn `Abbas (may Allah be pleased with him) who said: The Prophet (peace and blessings of Allah be upon him) said: “No woman should travel except with a Mahram , and no man should enter upon her unless there is a Mahram  with her.” A man said: “O Messenger of Allah, I want to go out with such and such an army and my wife wants to go for Hajj .” He said: “Go out with her.” 
Based on that, it is not permissible for a woman to travel to seek knowledge without a Mahram . She should acquire the knowledge that she needs in the many ways that are available, such as listening to tapes, asking scholars over the phone and other means that Allah has made available in these times. 
The Standing Committee was asked: Can a woman go out to study medicine, if it is obligatory or permissible, if doing so will lead to the following things no matter how much she tries to avoid them: 

Mixing with men, such as speaking to the patients, the tutor of medicine and on public transport.
Travelling from a country such as Sudan to Egypt, even if the journey will take only hours, and not three days.
Is it permissible for her to stay alone without a Mahram in order to learn medicine, if she is going to stay with a group of women, along with the circumstances described above?

They replied: 

“Firstly: if her going out to learn medicine will lead to her mixing with men during her study or when riding in mixed transportation that will lead to temptation, then it is not permissible for her to do that, because guarding her honour is an individual obligation, but learning medicine is a communal obligation, and an individual obligation takes precedence over a communal obligation. As for merely speaking to a patient or a teacher of medicine, that is not prohibited, rather what is prohibited is making the voice soft and appealing when speaking to him, which may tempt those in whose heart is the sickness of evil and hypocrisy. This does not apply only to learning medicine. 
Secondly: If she has a Mahram who can travel with her so that she can learn medicine, or teach it, or treat a patient, that is permissible. If she does not have a husband or Mahram who can travel with her, then it is prohibited, even if the journey is by plane, because the Prophet (peace and blessings of Allah be upon him) said: “No woman should travel except with a Mahram.” (Narrated by Al-Bukhari and Muslim). And because of what we have stated above about the interests of protecting honour taking precedence over the interests of learning medicine or teaching it, etc. 
Thirdly: If her staying with a trustworthy group of women is so that she may learn medicine or teach it, or treat women, then it is permissible, but if there is the fear of temptation because of not having a husband or Mahram with her, then it is not permissible. If she is going to treat men, that is not permissible unless it is a dire need and she is not alone with a man ." (Fatawa Al-Lajnah Ad-Daimah, 12/178) 

And Allah knows best.