From the Wikipedia page 
Copenhagen Municipality (Danish: Københavns Kommune), also known in English as the Municipality of Copenhagen, located in the Capital Region of Denmark, is the largest of the four municipalities that constitute the City of Copenhagen (Byen København), the other three being Dragør, Frederiksberg, and Tårnby. The Municipality of Copenhagen constitutes the historical city center and the majority of its landmarks. It is the most populous in the country with a population of 623,404 inhabitants (as of January 2019), and covers 86.4 square kilometres (33.4 sq mi) in area. Copenhagen Municipality is located at the Zealand and Amager islands and totally surrounds Frederiksberg Municipality on all sides. The strait of Øresund lies to the east. The city of Copenhagen has grown far beyond the municipal boundaries from 1901, when Frederiksberg Municipality was made an enclave within Copenhagen Municipality.
The municipal seat of government is the Copenhagen City Hall (Danish: Københavns Rådhus). The Lord Mayor of Copenhagen is Frank Jensen, since 2010. The relationship between Copenhagen Municipality and the wider city of Copenhagen is one of an administrative unit within a significantly larger city, cf. the City of London or the City of Brussels.
Copenhagen Municipality is distinct from the wider Copenhagen urban area. The seat of Copenhagen's municipal council is the Copenhagen City Hall (Rådhus). The council is chaired by the Lord Mayor—currently Frank Jensen—who oversees the civic duties of the fifty-five representatives of the council. The council usually meets every other week at 17:30 on a Thursday. They discuss a range of issues including labour and employment, business growth, economics, international cooperation and IT, urban planning, housing and construction, and young, old, and disabled peoples' issues, healthcare, and traffic, with a central focus on making the city sustainable and meeting environmental and health targets.[8
All members of the council are elected every four years. In the municipal elections in November 2013, the Social Democrats remained in first place with 27.8% of the vote (down by 2.2% from 2009), while the Red-Green Alliance was in second place with 19.5%. The Social Democrats have claimed the office of mayor for the past 110 years.
The municipal government is divided into seven administrative departments: Employment and Integration, Culture and Leisure, Health and Care, Finance, Child and Youth, Social Services, and Technical and Environmental Administration. It has six political committees and a finance committee. The annual budget for the city is proposed in August and finalized in October and the annual report is published in May of every year. The accounting firm Deloitte is responsible for auditing the City of Copenhagen's accounts.