Where and when did the decisive battle of the anti-Napoleonic coalition against the French army take place?

Where and when did the decisive battle of the anti-Napoleonic coalition against the French army take place? How did it end? Why do historians call this battle “the battle of the nations”?

The Battle of the Nations was carried out from 16.10. on 19.10.1813, it flared up near the city of Leipzig, located in the territory of Saxony. It resulted in the defeat of the Napoleonic military forces and the loss of the controlled lands by Napoleon I to the east of the Rhine. The French leader was left with only France, and the road to the invasion of the anti-French coalition was open. The battle is called the Battle of the Nations because of the motley national composition of its participants. This circumstance was typical for both fighting sides.