What is the ruling on a woman traveling and residing alone without a mahram for study or work in another city?

It is not permissible for a woman to travel alone without a mahram, due to the Prophet's (peace be upon him) saying: "It is not lawful for a woman who believes in Allah and the Last Day to travel for a distance of a night, unless she is accompanied by a mahram from among her relatives." As for her residing alone in the city, the basic principle is permissibility, but it is not advisable due to the abundance of dangers and harms in these times. A woman traveling for study without a mahram is not permissible according to Islamic law.