The Ministry of Magic
"The Ministry of Magic wishes you a pleasant day..."
-- the Welcome Witch's voice at Ministry Headquarters
The Ministry of Magic is the governmental authority for the Wizarding world in Britain. The basic mission of the Ministry is to keep the Muggles from finding out about an entire culture of magical folk. It's a huge, complicated, and inefficient bureaucracy, just like most governmental organizations.
The Ministry consists of seven departments of which the Department of Magical Law Enforcement is the largest. All of the other departments are in some way answerable to it, with the possible exception of the Department of Mysteries (FB).
The Ministry has its headquarters in London (PA11, OP7, DH12, 13 ). It consists of numerous Departments, Committees, Boards, and Offices whose job it is to make and enforce laws and regulations. Besides keeping the activities of Witches and Wizards hidden from the Muggles (and swooping in with Memory Charms when things get out of hand), the Ministry also handles commerce and international relations.
There are a number of law enforcement agencies within the Ministry. They maintain order, enforce laws and regulations, deal with breaches of security, and operate Azkaban, the wizard prison. This high-security fortress is located on a tiny island far out to sea. It is guarded by Dementors (PA5). The Ministry also maintains squads of Hit-Wizards to deal with criminals and elite Aurors to track down Dark wizards. The Wizengamot is the High Wizard Court, a body which serves as the ultimate arbiter of justice for the wizarding world.
The Muggle Prime Minister is aware of the wizarding world (HBP1) . Presumably this is also true of the President of the United States and of other world leaders. Both when Sirius Black (July 1993) (PA2) and when ten top Death Eaters (1996) (OP25) escaped from Azkaban, Cornelius Fudge informed the Prime Minister the escapees were dangerous wizards because he posed a threat to Muggles as well as magic folk. In extreme cases where a magical creature has been seen by Muggles and the usual interventions won't suffice, the Office of Misinformation (part of the Department for the Regulation and Control of Magical Creatures) works with the Muggle Prime Minister to concoct a believable lie to give to the public (FB, c.f. HBP1 ).
Links to further information:
Minister for Magic
Ministry Headquarters, London
Departments, committees, etc.
Rules and Regulations
History of the Ministry of Magic
Portkey search for references to the Ministry of Magic
Other countries have similar governing bodies; Bulgaria, for example, has its own Ministry of Magic, the Minister of which, Mr. Oblansk, sat in the Top Box to watch the World Cup Final in 1994 (GF8). There is also a Ministry of Magic in Norway (QA3) and other countries. All of these governmental organizations have signed the International Statute of Wizarding Secrecy of 1692 which set down many requirements for individual countries to keep the Muggles unaware of the wizarding world. This requires the Ministries of each country to monitor activities such as Quidditch and to protect and hide the various magical beasts which live within their borders (FB, QA).
International Federation of Warlocks (PA3)
Ministries of Magic: