Local government in Germany

There are five levels of government in Germany. The lowest two levels of the German government are called local government. The five levels of German government are all legally independent. This means that each level of government has a separate job in Germany. The German constitution (the Grundgesetz) lists the five levels of government and says what each level should do.
The five levels are:
The European Union (or EU). The EU can make laws that all the other levels of government must execute (do completely);
The Federation or national government. The national government of Germany is responsible for defense and Foreign policy. The national government develops standards about the actions of the sixteen Lander (states). The federation also gives money to poorer states. It is designed to help all states to be equal.
The sixteen Lander (states). The state government can create rules for local government in each state. But state governments cannot "abolish" (officially end) local governments. Local government is guaranteed by the constitution and the federal government;
The rural districts or counties (Landkreise) and the urban districts or independent towns;
The towns and municipalities, which are parts of a district or perhaps suburbs of an urban district.
Some states have Regierungsbezirke which are a group of counties and cities in an area to help run certain tasks across the area.
Other states have Amte which is a collection of municipalities (local governments) in a district. They might do this if the local governments are too small to run some local services.
Regierungsbezirke and Amte are not guaranteed by the constitution, they are a way of helping the various levels of government to do their job.
Subsidiarity
The idea of subsidiarity means that government jobs should be done by the lowest possible level.
There are two types of tasks (jobs) for a municipality. "Voluntary" which a town or municipality can do if it wants, and "mandatory", which are things that a federal or state law says the local government has to do.
Setting up a theatre, a museum, a sports field or a meeting hall is a voluntary task. If the local government can afford to set these things up, the Land (state) cannot stop them. Also the Land (state) cannot order the local government to set these things up.
The mandatory self-government tasks are things which a local government must do itself, or must get someone else to do for it. For example, one of the most important jobs of any local government is to prove its citizens (people who live there) with water, electricity, heating, and gas, as well as wastewater services and waste removal.
A council could run its own waterworks or join with others to share a larger facility. Modern electricity supply means that a council does not have to run their own power station anymore. But they must help private companies get the electricity supply to local houses and factories.
Transferred tasks
Although the Federation or state might have the right to control some things, the idea of subsidiarity means that they are administered (carried out) at the lowest possible level. For example, marriage ceremonies and issuing birth and death certificates are arranged by the town registrar, the Federation and the Land arrange legal and expert supervision so that the task is done properly and is the same across Germany.
Other transferred tasks include:
General security
Nationality, registration, passport affairs
Registrar's office and civil status
Commercial affairs
Construction matters
Health care, veterinary affairs
Road traffic
Registration of vehicles and vehicle taxation, (national and state laws say which cars can be registered, but local offices do the actual work)
Water legislation and land cultivation
Running Federal and Land parliamentary elections (roughly each district or kreis is a federal constituency, so voter registration and counting could be done by the district, but there are also larger Land based constituencies, so susidiarity make the Land the smallest possible level to handle counting)
Social security affairs, youth care. Social security rates are set by the federal government, but paid out by municipal authorities.
Protection and maintenance of historical monuments
Statistics
Forestry and fisheries.
Running local government
Who runs the town or district government depends on where in Germany the town is.
Magistrat system
The town council, or town council meeting is responsible for all jobs not given to the magistrat. The magistrat is the executive responsible for administering services. It is chosen by the town council, and can have both professional and honorary members. The mayor is head of the magistrate, but not of the town council meeting. The mayor is chosen separately by the people not the council. the system is only used in Hesse. It is the oldest system, and the only system where a group of elected people are responsible for the administration, instead of just one, the mayor.
Mayoral system
The mayor is head of the council and the administration.
North German system
Power is split between the mayor and the town clerk. The mayor has some functions, but day-to-day administration is done by the professional town clerk.
South German system
Used in Bavaria and the old eastern lander. The mayor is elected by the people, and he heads the council and the town government. The council is responsible for nearly all decisions. Some decisions are taken by the mayor. The council may give some of its tasks to the mayor, in which case they cannot change the mayor's decision.