Explanation:

The Quran states:
Do not marry polytheist woman until she believes; a slave believing woman is better than polytheist women though she allures you; Do not marry (your girls) to polytheist man until he believes: A man slave who believes is better than an polytheist man, even though he allures you. They do (but) beckon you to the Fire. But God beckons by His Grace to the Garden (of bliss) and forgiveness, and makes His Signs clear to mankind: so that they may understand.

When there come to you believing women refugees, examine (and test) them: God knows best as to their Faith: if ye ascertain that they are Believers, then send them not back to the Unbelievers. They are not lawful wives for the Unbelievers, nor are the Unbelievers lawful husbands for them.

It is lawful for Muslim men to marry Jewish or Christian women but not a polytheist woman

• Marriage between people of the same sex
• Marriage between a man and his sister, half-sister, foster sister, mother, stepmother, foster mother, wife's mother, aunt, grandmother, great aunt, great-grandmother, etc.
• Marriage between a woman and her father, stepfather, husband's biological father, uncle, grandfather, great uncle, great-grandfather, etc.
• Marriage of a man with women who are sisters or stepsisters or foster sisters of each other (except if marrying one who was separated from her husband by divorce or death)
• Marriage of a man with women who are sisters or stepsisters or even cousins of his mother or father.

Note: Marriage between cousins is not prohibited.