Can a non-muslim man marry a muslim woman?
It is absolutely not permissible under any circumstances in Islamic law (shari'a) of Allah, the most esteemed and exhalted, for a non-Muslim to marry a Muslim woman, as per what He has said regarding the marriage of a kafir (unbeliever) to a Muslim woman and vice versa: (interpretation of the meaning).
They are not lawful (wives) for the unbelievers, nor are the unbelievers lawful (husbands) for them... (Al-Mumtahina:10)
And Allah the most esteemed and exhalted has also said (interpretation of the meaning):
Nor marry (your girls) to unbelievers until they believe... (Al-Baqara:221)
i.e., it is not ever permissable for someone to marry his Muslim daughter or sister or any Muslim woman for whom he is a guardian to a kafir.
Islam must be exhalted and cannot be subjugated, so how could a Muslim woman be put under the care of a kafir man, when the man is normally naturally in a stronger position? In such a situation he could cause her to corrupt the practice of her religion or force her into subdual by causing her to live a life of oppression with him. He could also prevent her from practicing some of her religious rites. These are among the reasons for the aforementioned ban expressed in the previous ayaat. wallahu a'lam (and Allah is the most knowledgable).