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In Islam, a mahram is a member of one's family with whom marriage would be considered haram (illegal in Islam); from whom purdah, or concealment of the body with hijab, is not obligatory; and with whom, if he is an adult male, she may be escorted during a journey, although an escort may not be obligatory.
(Note: A woman may marry her stepfather only if the stepfather has not consummated his marriage to her mother.)
When a woman acts as a wetnurse (that is she breast feeds an infant that is not her own child for a certain amount of time under certain conditions), she becomes the child's rada mother and everything concerning blood mahrams applies here, like rada father/mother, rada sister/brother, rada aunt/uncle and so on. In English these can be referred to as milk brother, milk-mother, and so on. For a man, mahram women include his mother, grandmother, daughter, granddaughter, sister, aunt, grandaunt, niece, grandniece, his father's wife, his wife's daughter (step-daughter), his mother-in-law, his rada mother and any other rada relatives that correspond to the above-mentioned blood relatives. As the Prophet Mohamed said, "What is forbidden by reason of kinship is forbidden by reason of suckling."
These are considered mahram because they are mentioned in the Quran (An-Nisa 22-23):
"And marry not women whom your fathers married, except what has already passed; indeed it was shameful and most hateful, and an evil way. Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your paternal aunts, your maternal aunts, brother's daughters, sister's daughters, your foster mothers, your sisters from suckling, mothers of your spouses, your step-daughters from your those spouses you have entered into them but if you have not entered into them then there is no blame on you, spouses of your sons from your own loins and that you add two sisters except that has passed; indeed God is forgiving and merciful."
All of the man's female relatives mentioned in these two verses are considered his maharim, because it is unlawful (haram) for him to marry them, except the wife's sister, whom he can marry if he divorces her sister, or if his wife dies. The notion of mahram is reciprocal. All other relatives are considered non-maharim.
See also: Women in Islam § Movement and travel
A woman may be legally escorted during a journey by her husband, or by any sane, adult male mahram by blood, although an escort may not be required, including
A Muslim woman's mahrams form the group of allowable escorts when she travels. An adopted brother who suckled from the mother of the woman is axiomatically a mahram.
For a spouse, being mahram is a permanent condition. That means, for example, that a man will remain mahram to his ex-mother-in-law after divorcing her daughter.
An adopted sibling is ghayr mahram, and marriage is allowed to an adopted sibling of the opposite sex. The term "adopted" means those children who are adopted by one's parents for the purpose of providing shelter and upbringing and who do not fall under the relationships outlined under the section "Who is mahram?" above.
One is ghayr mahram to one's ex-spouse.
One must not stay with a ghayr mahram in seclusion where none of their mahrams is present (see also proxemics).
If wives of a man each become a rada mother of a child, all children and all rada mothers will be mahram to each other.