Arguably the most important of the various departments, the Department of Magical Law Enforcement is a combination of police and justice facilities. It is located on the second level of the Ministry of Magic.

You may find Auror Office, Improper Use of Magic Office, Wizengamot, and other offices here.

As noted in Fantastic Beasts and Where to Find Them, the Department for the Regulation and Control of Magical Creatures is divided into three divisions (the Beast Division, the Being Division, and the Spirit Division) and contains the Goblin Liaison Office and Centaur Liaison Office, though the centaurs, being isolationists, have never interacted with the office since its creation. Thus, "being sent to the Centaur Office" has become a euphemism at the Ministry for those about to be fired.[HPF] For further detail on the distinctions between these divisions, see Regulation and classification of Magical creatures.

The Department of International Magical Cooperation is an agency that attempts to get wizards from different countries to cooperate in wizarding actions both political and public.[HP4] This department on the fifth level of the Ministry of Magic includes the headquarters of the International Magical Trading Standards Body, the International Magical Office of Law, and the British seats of the International Confederation of Wizards. The former head was Barty Crouch, Sr., until his death. This is also where Percy Weasley began his Ministry career.

This department is similar in function to the real-life British Foreign and Commonwealth Office, and various organs of the United Nations.

Duties

work with magical governments of other countries
sets standards for trade
creates regulations for things like cauldron thickness
worked with Department of Magical Games and Sports on the Triwizard Tournament
International Confederation of Wizards, British Seats.

The Department of Magical Transportation is responsible for various aspects of magical transport. It is located on the sixth level of the Ministry of Magic and includes the following offices: the Floo Network Authority, responsible for setting up and maintaining the network, and distributing the greenish floo powder; the Broom Regulatory Control, that controls the traffic of broom travel; the Portkey Office, the regulation of Portkeys; and the Apparition Test Centre, that grants licences to witches and wizards so that they can apparate.

The Department of Magical Games and Sports, seen as the most relaxed department (posters for favourite Quidditch teams are found tacked to the walls), deals with organising sports events the likes of the Quidditch World Cup and the Triwizard Tournament. Ludo Bagman used to be the Head of Department here, but his gambling problem forced him to flee from Goblin creditors. The department is located on the seventh level of the Ministry of Magic, and includes the British and Irish Quidditch League Headquarters, Official Gobstones Club, and the Ludicrous Patents Office – other sports and games-related aspects.

The Department of Mysteries, located on Level Nine is a department in the Ministry of Magic which studies particular enigmas (death, time, space, thought, and love) and stores copies of prophecies made in the Harry Potter universe. During Voldemort's discriminatory regime, he forces the department to lie and claim that Muggle-borns actually steal magic from Pure-bloods, making them "illegal magicals" and allowing their arrest.

Because of the covert nature surrounding this particular branch of the Wizarding government, the Department of Mysteries can be likened to real-world intelligence agencies like the CIA or MI6, in that most of their operations are kept in total secrecy from the general wizard populace. However, the primary operations of the department seem to be more like those of scientists, the department attempting to uncover the sources and rules that govern magic.