Final answer:
The European nations forced Russia to relinquish its territorial gains after the Crimean War to maintain a balance of power and ensure European peace and stability, as Russia's expansion was seen as a threat to the established order.
Step-by-step explanation:
A congress of European nations in 1856 forced Russia to give up the territorial gains it made during the Crimean War primarily to maintain a balance of power in Europe. After the war, it became evident that Russia's attempts to expand in the Black Sea region during the political decline of the Ottoman Empire were seen as a threat to this balance by other European powers, including France and Britain.
Moreover, the war exposed Russia's military and infrastructural weaknesses, undermining its position and prompting other European nations to act to prevent its dominance.
The Congress System was focused on ensuring peace, and stability, and maintaining the status quo following the turmoil of the Napoleonic Wars. The Congress of Vienna and subsequent agreements were designed to distribute power evenly among the great powers of Europe to prevent one nation from becoming too influential, which Russia's territorial ambitions directly challenged.
Therefore, the European Congress's decision to curtail Russia's gains was in line with the overarching goal of European peace and stability.