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.