How did the French Revolution initiate wars that led to the Congress of Vienna?
You will remember that Louis XVI was executed by his own people during the French Revolution. Other crown heads of Europe feared, correctly it seems, that the revolution would spread to the rest of Europe. For this reason, they hoped to restore the French Monarchy. A number of European powers, notably Austria and Britain, attempted to intervene and return the King to power. They had help from a number of royalists in France and others who led an army against the Directory. That insurrection was defeated by Napoleon Bonaparte with his famous "whiff of grapeshot."
The government was so weak that Napoleon had no difficulty disposing of it and acting on his own authority as head of the military. He thereafter commenced a campaign against the rest of Europe, destroying the Holy Roman Empire, and only ending his campaigns after his defeat at Austerlitz and later Waterloo. The forces who opposed Napoleon were the other heads of European states, namely England, Prussia and Russia, who were intent on preserving the balance of power. The Roman Empire had been the last entity to rule all of Western Europe; and they were determined to see that such rule did not happen again.
After Napoleon's final defeat, the victorious powers met at Vienna in an attempt to restore the old order which had previously existed. They were led by Klaus von Metternich of Austria. None of this would have been necessary had it not been for the fall of the French monarchy during the revolution.
After the French Revolution, Napoleon Bonaparte came to power in France. Napoleon wanted to create an empire for himself that would eventually encompass much of Europe. It was this ambition that led to the wars.
As he came to power, Napoleon expanded his influence in Europe. This expansion made various other European powers very anxious. Among these were the British, the Austrians, the Russians and the Prussians. All of these feared that an enlarged France would endanger them.
These four powers engaged in a series of wars against Napoleon. After the wars ended, they met at the Congress of Vienna to decide between themselves what Europe would look like after Napoleon was defeated.