She has the right to inherit from her father, mother, and husband. A very interesting point to note is that in Islam, unlike any other religion, a woman can be an imam, a leader of communal prayer, for a group of women. A Muslim woman also has obligations. All the laws and regulations pertaining to prayer, fasting, charity, pilgrimage, doing good deeds, etc., apply to women, albeit with minor differences having mainly to do with female physiology. Before marriage, a woman has the right to choose her husband.
Islamic law is very strict regarding the necessity of having the woman's consent for marriage.
She keeps her own family name, rather than taking her husband's. As a wife, a woman has the right to be supported by her husband even if she is already rich. She also has the right to seek divorce and custody of young children. She does not return the dowry, except in a few unusual situations. Despite the fact that in many places and times Muslim communities have not always adhered to all or even many of the foregoing in practice, the ideal has been there for 1400 years, while virtually all other major civilizations did not begin to address these issues or change their negative attitudes until the 19th and 20th centuries, and there are still many contemporary civilizations which have yet to do so.