Answer:
The rule, per Islam religion, is that Muslim man is allowed to marry a woman of any of the three religions Islam, Christianity (Catholics, Orthodox, ... or other denominations), and Judaism. He is forbidden to marry any woman from any religion other than these three religions.
However, a Muslim girl is allowed to get married with only a Muslim man and she is forbidden to get married with a man of any different religion.
Hint: Some other people have the view point that any person of any faith can marry anyone they want and that love conquers all, even religion. However, this is true only if you are not committed to a religion with God or not believing in God at all. If you are committed with God through any religion, what so ever, you have to fulfill this commitment. This is in analogy to one committed with an employer through a work contract (despite the difference between commitment in contract with God, the Creator, and commitment in contract with an employer, creature). Does falling in love with someone entitle you not to go for work or not to fulfill your work commitment? The same answer applies to your commitment with God when you fall in love and thinking of marriage. On the other hand, of course you have full right and full choice to select either to fulfill religion commitment or to abandon the religion you committed to and throw it behind. However, choice is responsibility. You should be aware that your choice defines the consequences that you get.
That explains how and why Islam spreads through assertive domination and multiplication. Islam's man can marry non-muslim women so their children should be claimed for Islam besides Islam's man can marry until four women provided he's able to. Non-muslim men cannot have a muslim woman unless converting to Islam first. What a vacuous bargain, discrimination and blatant sexism.