Restore peace and stability to Europe
The delegates of the Congress of Vienna were interested in creating a balance of power in European politics. They did not want one nation to become too powerful again and press beyond its borders as France had done under Napoleon. The Congress of Vienna emphasized also the principal of "legitimacy" -- trying to put rulers in power that they thought to be the legitimate rulers of nations. (So, for instance, the Bourbon monarchy was restored in France.) They sought to prevent revolutions and unrest from breaking out again ... but it would only be a couple decades before further revolutions did occur.
