Short answers, pulled from the story.
The European balance of power is a principle in international relations holding that no single state should be allowed to achieve hegemony over a substantial part of Europe. It was enforced through ever-changing alliances among competing powers across centuries of European history.
The doctrine developed gradually through practical experience rather than from any single founding moment. Its roots are traced back to ancient Greek city-states and the power struggles of the Roman Republic, but it became a formally recognized principle of European diplomacy from the Peace of Westphalia in 1648 onward.
The Concert of Europe was the system established at the Congress of Vienna in 1815 by the victorious Great Powers, Prussia, Austria, Russia, and Great Britain, to maintain the European balance of power after the Napoleonic Wars. Historian Roy Bridge judged that it had "failed" by 1823, and historian Artz identified the Congress of Verona in 1822 as marking its end.
The stately quadrille refers to the 18th-century pattern in which the four major European powers, Austria, Prussia, Great Britain, and France, repeatedly shifted alliances to prevent any one of them from achieving dominance. Wars including the War of the Spanish Succession, the Seven Years' War, and the War of the Austrian Succession were driven at least in part by this logic.
The Thirty Years' War, fought from 1618 to 1648, killed between 4.5 and 8 million people and caused population declines of over 50% in some German regions. The Treaty of Westphalia that ended it decentralized the Holy Roman Empire, elevated France to the leading continental power, and established Sweden and France as formal guarantors of the imperial constitution.
Lord Ismay, the British first Secretary General of NATO, stated the organization's initial goal was "to keep the Russians out, the Americans in, and the Germans down." This phrasing summarized how the post-World War II balance of power was institutionalized through the Western alliance.