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In addition to the prohibition of marrying a mamzer, there are marriage prohibitions binding upon all Jews, primarily the ban on marrying first-degree relatives.
If a married woman willingly had relations with someone other than her husband, she becomes prohibited to her husband and they must divorce. She also may not marry the man with whom she committed adultery. These laws are complex; sometimes it is possible to find ways to be lenient.
Intermarriage is a serious transgression. Not only that, it is also likely to lead to assimilation. If children are born as a result of such a relationship, their status follows that of the mother. If the mother is Jewish, so are the children; if she is non-Jewish, so are the children. However, if the children of a mixed marriage are interested in converting, they are encouraged to do so, since their father is Jewish.
Priests (men descended from Aaron) have additional restrictions, since they were consecrated to work in the Temple. A priest may not marry a convert, a divorcee, a woman who has undergone the ĥalitza ritual (a symbolic separation ritual performed when a man dies childless and his widow does not want to marry his brother), a woman who has committed incest, or a woman who has had relations with a non-Jew. If a priest married a woman forbidden to him, their daughter may not marry a priest, nor may the daughter of their male descendants. Yet a priest’s daughter is not limited; any man who is permitted to marry a Jewish woman may marry a priest’s daughter.
