Question: The Treaty of Vienna, concluded on 27 May 1657, was an Austro–Polish alliance during the Second Northern War, the House of Habsburg, also called House of Austria, was one of the most influential and outstanding royal houses of where?

Context articles: Treaty of Copenhagen (1660)
Treaty of Vienna (1656)
House of Habsburg
Second Northern War
Treaty of Vienna (1657)
Treaty of Rinsk
Truce of Vilna
Treaty of Elbing
Treaty of Kėdainiai
Dano-Swedish War (1657–58)

The Treaty of Copenhagen was signed on 27 May 1660, and marked the conclusion of the Second Northern War between Sweden and the alliance of Denmark-Norway and the Polish-Lithuanian Commonwealth.
 This treaty was a smaller follow-up treaty to that of the Treaty of Roskilde, which decisively delineated the mutually recognized boundaries of Denmark, Sweden, and Norway; boundaries which are almost exactly the same to this day.
The treaty of Vienna, concluded on 1 December 1656, was an Austro–Polish alliance during the Second Northern War.
 Habsburg emperor Ferdinand III agreed to enter the war on the anti-Swedish side and support the Polish king John II Casimir with 4,000 troops.
 The treaty was, however, dissatisfying for John II Casimir, who had hoped for more substantial aid, and further ineffective as Ferdinand III died three days after giving his signature.
 A similar, but more effective alliance was concluded by Ferdinand III's successor Leopold I in the Treaty of Vienna (1657).
The House of Habsburg ( ; ] ), also called House of Austria, was one of the most influential and outstanding royal houses of Europe.
 The throne of the Holy Roman Empire was continuously occupied by the Habsburgs between 1438 and 1740.
 The house also produced emperors and kings of the Kingdom of Bohemia, Kingdom of England ("Jure uxoris" King), Kingdom of Germany, Kingdom of Hungary, Kingdom of Croatia, Second Mexican Empire, Kingdom of Ireland ("Jure uxoris" King), Kingdom of Portugal, and Spain, as well as rulers of several Dutch and Italian principalities.
 From the 16th century, following the reign of Charles V, the dynasty was split between its Austrian and Spanish branches.
 Although they ruled distinct territories, they nevertheless maintained close relations and frequently intermarried.
The Second Northern War (1655–60, also First or Little Northern War) was fought between Sweden and its adversaries the Polish–Lithuanian Commonwealth (1655–60), Russia (1656–58), Brandenburg-Prussia (1657–60), the Habsburg Monarchy (1657–60) and Denmark–Norway (1657–58 and 1658–60).
 The Dutch Republic often intervened against Sweden.
The Treaty of Vienna, concluded on 27 May 1657, was an Austro–Polish alliance during the Second Northern War.
 After Habsburg emperor Ferdinand III had agreed to
The treaty of Rinsk, concluded on 2 November (O.S.) / 12 November (N.S.) 1655, was a Ducal-Royal Prussian alliance during the Second Northern War.
 Frederick William I, Elector of Brandenburg and duke of Prussia, and the nobles of Royal Prussia agreed to allow Brandenburgian garrisons in Royal Prussia to defend it against the imminent Swedish invasion.
 The important towns of Danzig (Gdańsk), Thorn (Toruń) and Elbing (Elbląg) did not participate in the treaty and were not garrisoned by Brandenburgian troops, and except for Danzig surrendered to Sweden.
 The remainder of Royal Prussia, except for Marienburg (Malbork) was overrun by Sweden and Frederick William I's forces pursued to Königsberg (now Kaliningrad), where he was forced to accept Swedish overlordship in the Treaty of Königsberg in January 1656.
Truce/Treaty of Vilna or Truce/Treaty of Niemieża (Polish: "Rozejm w Niemieży" ) was a treaty signed at Niemieża (modern Nemėžis) near Vilnius (also known as Vilna) on 3 November 1656 between Tsardom of Russia and Polish–Lithuanian Commonwealth, introducing a truce during the Russo-Polish War (1654–67) and an anti-Swedish alliance in the contemporaneous Second Northern War.
 In return for ceasing hostilities and fighting Sweden alongside Poland–Lithuania, the treaty promised Alexis of Russia succession in Poland after John II Casimir Vasa's death.
 The cossacks under Bohdan Khmelnytsky were excluded from the negotiations, and subsequently supported the Transylvanian invasion on the Swedish side.
The Treaty of Elbing was signed between the Dutch Republic and the Swedish Empire on 1 September (OS) / 11 September 1656, during the Second Northern War, in Swedish-held Elbing (Elbląg).
 It served to protect Dutch interests in the Baltic Sea, ended the Dutch intervention in the Swedish siege of Danzig, and renewed a fragile peace between the Dutch Republic and Sweden.
 Within the former, there was opposition to the treaty demanding elucidations, which were agreed upon only on 29 November (OS) / 9 December 1659 in the Convention of Helsingör.
 Earlier in 1659, in the Concert of The Hague, England, France, and the Dutch Republic had agreed to include the treaty of Elbing in their common agenda regarding the Second Northern War.
The Treaty of Kėdainiai or Kiejdany, signed on 17 August 1655, was a Swedish–Lithuanian agreement during the Second Northern War.
 After the Polish forces had been decisively defeated in the Battle of Ujście, whereupon the Poznań and Kalisz palatines surrendered to Sweden, Lithuanian hetman Janusz Radziwiłł decided to discontinue the war.
 In Kėdainiai, he accepted Swedish protection.
 The treaty further specified that the Polish–Lithuanian Commonwealth was not dissolved and Lithuanian forces would not fight Polish forces, although the text of the treaty included protests against the lack of Polish support.
 On 20 October, the treaty was superseded by the Union of Kėdainiai, which united the Grand Duchy of Lithuania with the Swedish Empire.
The Dano-Swedish War of 1657–58 was a conflict between Sweden and Denmark–Norway during the Second Northern War.
 In 1657, Charles X of Sweden and his Swedish army were bogged down in Poland.
 Frederick III of Denmark saw an opportunity to recover the territories lost in 1645 and attacked Sweden.
 The outbreak of war with Denmark provided Charles with an excuse to withdraw from the Polish campaign and move against Denmark.