Brandenburg-Prussia instance of state in the Holy Roman Empire
Brandenburg-Prussia (German: Brandenburg-Preußen; Low German: Brannenborg-Preußen) is the historiographic denomination for the early modern realm of the Brandenburgian Hohenzollerns between 1618 and 1701. Based in the Electorate of Brandenburg, the main branch of the Hohenzollern intermarried with the branch ruling the Duchy of Prussia, and secured succession upon the latter's extinction in the male line in 1618. Another consequence of the intermarriage was the incorporation of the lower Rhenish principalities of Cleves, Mark and Ravensberg after the Treaty of Xanten in 1614.
The Thirty Years' War (1618–1648) was especially devastating. The Elector changed sides three times, and as a result Protestant and Catholic armies swept the land back and forth, killing, burning, seizing men and taking the food supplies.  Upwards of half the population was killed or dislocated.  Berlin and the other major cities were in ruins, and recovery took decades. By the Peace of Westphalia, which ended the Thirty Years' War in 1648, Brandenburg gained Minden and Halberstadt, also the succession in Farther Pomerania (incorporated in 1653) and the Duchy of Magdeburg (incorporated in 1680). With the Treaty of Bromberg (1657), concluded during the Second Northern War, the electors were freed of Polish vassalage for the Duchy of Prussia and gained Lauenburg–Bütow and Draheim. The Treaty of Saint-Germain-en-Laye (1679) expanded Brandenburgian Pomerania to the lower Oder.
The second half of the 17th century laid the basis for Prussia to become one of the great players in European politics. The emerging Brandenburg-Prussian military potential, based on the introduction of a standing army in 1653, was symbolized by the widely noted victories in Warsaw (1656) and Fehrbellin (1675) and by the Great Sleigh Drive (1678). Brandenburg-Prussia also established a navy and German colonies in the Brandenburger Gold Coast and Arguin. Frederick William, known as "The Great Elector", opened Brandenburg-Prussia to large-scale immigration ("Peuplierung") of mostly Protestant refugees from all across Europe ("Exulanten"), most notably Huguenot immigration following the Edict of Potsdam. Frederick William also started to centralize Brandenburg-Prussia's administration and reduce the influence of the estates.
In 1701, Frederick III, Elector of Brandenburg, succeeded in elevating his status to King in Prussia. This was made possible by the Duchy of Prussia's sovereign status outside the Holy Roman Empire of the German Nation, and approval by the Habsburg emperor and other European royals in the course of forming alliances for the War of the Spanish Succession and the Great Northern War.  From 1701 onward, the Hohenzollern domains were referred to as the Kingdom of Prussia, or simply Prussia.  Legally, the personal union between Brandenburg and Prussia continued until the dissolution of the Holy Roman Empire in 1806.  However, by this time the emperor's overlordship over the empire had become a legal fiction.  Hence, after 1701, Brandenburg was de facto treated as part of the Prussian kingdom.  Frederick and his successors continued to centralize and expand the state, transforming the personal union of politically diverse principalities typical for the Brandenburg-Prussian era into a system of provinces subordinate to Berlin.Establishment under John Sigismund (1618)
The Margraviate of Brandenburg had been the seat of the main branch of the Hohenzollerns, who were prince-electors in the Holy Roman Empire, since 1415. In 1525, by the Treaty of Krakow, the Duchy of Prussia was created through partial secularization of the State of the Teutonic Order. It was a vassal of the Kingdom of Poland and was governed by Duke Albert of Prussia, a member of a cadet branch of the House of Hohenzollern. On behalf of her mother Elisabeth of the Brandenburgian Hohenzollern, Anna Marie of Brunswick-Lüneburg became Albert's second wife in 1550, and bore him his successor Albert Frederick. In 1563, the Brandenburgian branch of the Hohenzollern was granted the right of succession by the Polish crown. Albert Frederick became duke of Prussia after Albert's death in 1568. His mother died in the same year, and thereafter he showed signs of mental disorder. Because of the duke's illness, Prussia was governed by Albert's nephew George Frederick of Hohenzollern-Ansbach-Jägersdorf (1577–1603). In 1573, Albert Frederick married Marie Eleonore of Jülich-Cleves-Berg, with whom he had several daughters.In 1594, Albert Frederick's then 14-year-old daughter Anna married the son of Joachim Frederick of Hohenzollern-Brandenburg, John Sigismund. The marriage ensured the right of succession in the Prussian duchy as well as in Cleves. Upon George Frederick's death in 1603, the regency of the Prussian duchy passed to Joachim Frederick. Also in 1603, the Treaty of Gera was concluded by the members of the House of Hohenzollern, ruling that their territories were not to be internally divided in the future.The Electors of Brandenburg inherited the Duchy of Prussia upon Albert Frederick's death in 1618, but the duchy continued to be held as a fief under the Polish Crown until 1656/7. Since John Sigismund had suffered a stroke in 1616 and as a consequence was severely handicapped physically as well as mentally, his wife Anna ruled the Duchy of Prussia in his name until John Sigismund died of a second stroke in 1619, aged 47.
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