Madam, Madame, ma'am, or Mme is a title for a woman. It is derived from the French madame (see different meanings of madame here), the equivalent of Mrs. or Ms., and literally signifying "my lady." The plural of madam in this sense is mesdames. The French madame is in turn derived from the Latin mea domina meaning 'my mistress' of the home (domus). "Madam" may also refer to a woman who runs a brothel.
After addressing her as "Your Majesty," it is proper to address The Queen of the United Kingdom as "Ma'am" for the remainder of the conversation, with the pronunciation as in "ham" and not as in "farm".
Usage of "Ma'am" is common in the Southern United States.
However, the title Madam Justice is used in third-person reference: Madam Justice Louise Arbour, Madam Justice Arbour.
In the United States Supreme Court, rather than adopting the title Madam Justice for female justices, the title Mr Justice was replaced simply by Justice. Likewise, female presidents of the Republic of Ireland have preferred to be addressed simply as President in direct address, rather than Madam President. Female judges of the High Court of Justice of England and Wales are titled Mrs Justice rather than Madam Justice, regardless of marital status. However, District Judges are referred to as either Madam or Ma'am.
In the United States Armed Forces, "ma'am" is used to address female commissioned officers and Warrant Officers. U.S. Marine recruits and U.S. Air Force trainees also address female non-commissioned officers as "ma'am."