Marriage is often viewed as the union of two people, a man and a woman, who have decided to stay together.   But the functions and types of marriage are different from one culture to another.
In the Western world, a legal marriage is an agreement entered voluntarily between two people who are emotionally attached to each other.  This marriage should be monogamous, that is involving only two people.  To end such marriage, divorce is used.
In the Eastern world, some societies allow polygamy, a marriage that permits a man to have more than one wife.  Having multiple wives is a status symbol, indicating that the man has wealth and power.
In Indonesia, marriage is allowed between two people of the same faith.  Those with no religion, the atheists, are not allowed to marry.  In China, during the Imperial times, marriages in the upper classes are arranged.  This is celebrated with as much grandeur that the marrying families can afford.  Then, the husband is allowed to take other women as wives or concubines.  However, only the children of the primary wife are considered legitimate.  Later, to control overpopulation, the government of China only gives permits to monogamous marriages.
In Muslim societies, a man is allowed to have up to four wives.  There are reasons not related to attraction that make a Muslim take another wife.  For example, a brother dies leaving behind a wife who has no financial means to support herself.  The living brother, who already has a wife, may marry his brother’s widow in order to honor his brother.
In few tribal societies, such as some groups of Canadian Inuit, polyandry is practiced.  In polyandry, a woman is allowed to have more than one husband.  But this marriage type is rarely practiced nowadays.  Another rare marriage practice is simply called “group marriage” in which husbands are shared by several wives, and wives are shared by several husbands.  This was practiced by the Oneida community.  And still another rare type of marriage is called “marriage by abduction”, in which a woman who was kidnapped and raped, is forced to marry her rapist.  Feminists frown upon this type of marriage and no self-respecting cosmopolite would entertain such form of marriage.
How about same-sex marriage?  Same sex marriages are rare, and practically nonexistent in many cultures.  Many countries have declared it illegal.  But, as time goes by, some countries have permitted it.  These countries are the Netherlands, Belgium, Canada, and Spain.  A version similar to it is called “Civil Unions”.  It is recognized in Denmark, Norway, Sweden, Finland, Iceland, Germany, Greenland, France, New Zealand, and Portugal.