The Napoleonic wars were a series of wars fought between the Coalition and the French Empire. In all, there were 6 major Napoleonic wars.
The first war in the Napoleonic wars was the War of the Third Coalition. It was called that way because two Coalition wars were fought before Napoleon came on the scene. This war was fought from 1803 to 1806 and ended in a French victory. In the peace treaty, Austria recognized territory taken by France.
The War of the Fourth Coalition lasted from 1806 to 1807 and ended in another French victory. This war started because Prussia declared war on France because of the results of the War of the Third Coalition.
The Peninsular War lasted from 1807 to 1814. This war started because France wanted to conquer Spain during a Civil War, and England and Portugal joined the fray to stop that from happening. Due to Napoleon's failure, he was exiled to the island of Elba.
The War of the Fifth Coalition was fought in 1809. This war started because of France's involvement in the Peninsular War. Austria decided that France could not be trusted and the best way to avoid being done in in the same fashion would be to declare war on France first. France won this war, and Austria lost 3 million inhabitants, roughly 20% of the nation's population.
The French Invasion of Russia was fought in 1812. During this time, Napoleon tried to invade Russia, but discovered (like the Germans in WW2) that land's most effective defense, the winter. Napoleon and his 623,000 strong Grande Armeé took Moscow, but the Russians took everything of value and the army started starving. Napoleon had to retreat, losing ~410,000 men.
The War of the Sixth Coalition started in 1813 and ended in 1814. This war started when Britain, Russia, and Sweden formed an alliance against France, and many of France's allies were considering joining their side, not wanting to repeat the disastrous invasion of Russia. Napoleon was defeated again at Waterloo, which ended the Napoleonic Wars.