Amt

Amt is a type of administrative division governing a group of municipalities, today only in Germany, but formerly also common in other countries of Northern Europe. Its size and functions differ by country and the term is roughly equivalent to a US township or county or English shire district.
Current usage.
Germany.
Prevalence.
The "Amt" (plural: "Ämter") is unique to the German "Bundesländer" (federal states) of Schleswig-Holstein, Mecklenburg-Western Pomerania and Brandenburg.
Other German states had this division in the past. Some states have similar administrative units called "Samtgemeinde" (Lower Saxony), "Verbandsgemeinde" (Rhineland-Palatinate) or "Verwaltungsgemeinschaft" (Baden-Württemberg, Bavaria, Saxony, Saxony-Anhalt, Thuringia).
Definition.
An "Amt", as well as the other above-mentioned units, is subordinate to a "Kreis" (district) and is a collection of municipalities. The amt is lower than district-level government but higher than municipal government, and may be described as a supra-municipality or "municipal confederation". Normally, it consists of very small municipalities ("Gemeinden", plural of Gemeinde).
Larger municipalities do not belong to an "Amt" and are called "amtsfreie Gemeinden" (independent municipalities); some of these municipalities may also not depend from a "Kreis" (district) and are called "kreisfreie Gemeinden", and when they do also not belong to any other "Land" they are also called "Stadtstaaten" (plural of "Stadtstaat"), i.e. city-states (Berlin and Hamburg).
These large municipalities (cities, in German "Städte", plural of "Stadt") may be further divided into local offices named "Ortsämter" (plural of "Ortsamt"), each of them possibly grouping several suburbs (or small townships in rural areas) of the municipality named "Ortsteile" (plural of "Ortsteil"), named from small villages or hamlets or localities. The "Ortsteil" (suburb or township) may have been a former parish, but today it is meant only for civil purpose and essentially used for planning within the municipality; the "Ortsamt" (sometimes just named informally but confusingly as an "Amt", or informally translated as an "urban district") is used to offer decentralized services of the municipality within local administrative offices for the residents in neighbouring suburbs. The "Ortsteil" itself may also be confusingly translated as a "municipality", but it is incorrect because it belongs to a city which is the only effective municipality ("Gemeinde").
Former usage.
Denmark.
The ' (plural, '; commonly translated as "province" or, less accurately, "county") was an administrative unit of Denmark (and, historically, of Denmark-Norway). The provinces were established by royal decree in 1662 as replacements for the former ' (fiefs). The ' were originally composed of independent towns (') and parishes, and held only small areas of responsibility. During the 20th century, they were granted responsibility for the hospital service for the non-urban population. A 1970 administrative reform reduced the number of provinces to fourteen and eliminated the administrative distinction between (rural) parish and town. From then on, the "amter" were composed of a number of municipalities ('). The reform granted the provinces wider areas of responsibility, most notably running the national health service and the "gymnasium" secondary schools.
The Danish Municipal Reform of 1 January 2007 abolished the "amter" and replaced them with five administrative regions, now solely charged with running the national health service. In contrast to the "amter" the regions hold no authority to levy taxes. The reform re-delegated all other areas of responsibility to either the municipalities or the state. At the same time, smaller municipalities were merged into larger units, cutting the number of municipalities from 270 to 98. See Counties of Denmark for more information about the Danish usage of the term.
Germany.
In Germany an "Amt" was a medieval administrative district covering a manorial estate or the land owned by a castle or village. It was headed by an "Amtmann", usually a lesser nobleman or cleric, appointed by a territorial lord to administer and dispense justice within the "Amt".
Iceland.
While Iceland was a territory of the Danish-Norwegian realm, amts (singular: '; plural: ') were established in the country on top of the existing counties. From 1684 to 1770, Iceland as whole was a single amt in the Kingdom of Denmark-Norway but was then split into two amts: North and East Amt (') and South and West Amt ('). The latter was in 1787 split into a West Amt (') and South Amt ('). Iceland was thus divided into three amts until 1872, when the South and West amts were again merged. Amts were abolished in 1904, when Iceland gained home rule from Denmark.
Amts are not used to denote a geographical region in Iceland but the name lives on in the names of two public libraries in Iceland that were established during the amt era. The Amts libraries in Akureyri and Stykkishólmur which were established as the designated archives for the North and East Amt and the West Amt respectively.
Netherlands and Flanders.
"Ambacht" can be seen as the Dutch equivalent to "amt". "Ambachten" existed in Holland, Zeeland and Flanders up to about 1800.
Norway.
From 1662 to 1919, the counties of Norway were called "amter". They are now referred to as "fylker", a term revived from the Middle Ages.