The American Revolution
Just off of the top of my head, it is clear that the biggest event going on in this time was the American Revolution, which occurred from 1775-1783. It started with the British telling the colonists not to fraternize with the Indians. Then came the Proclamation Act of 1763. This enraged the colonists, because of course as soon as they were banned from doing something, that was exactly what they wanted to do. Then, as if to anger the colonists more, the passed the Stamp Act, in which they were basically taxing the colonists to fund soldiers that the colonists didn't want in America in the first place. Later, with the Townshend Acts, they repealed their taxes on Stamps and placed them instead on glass, lead, paints, paper, and tea. After extreme backlash from the colonies, they repealed all of the taxes except the ones on tea, and they forced the colonists to only buy tea from them. Because of that, the colonists were extremely angry and destroyed all the tea by dumping it into the Boston Harbor. This, of course, enraged the British, who then shut down the harbor and forced the colonies to pay them back for their losses, which was the equivalent of 1,374,083 American dollars in today's money. Of course, the Americans were having none of that. They prepared themselves for the British to attack. On April 19, 1775, the British started marching into Concord. On the way was Lexington, the place in which "the shot heard 'round the world" was fired and the American Revolution started. After approximately 242 battles and 25,000 dead, the war ended. America became an independent nation on July 4, 1776 with the signing of the Declaration of Independence, and again on September 3, 1783 when the war ended.
Napoleonic Wars
On December 12, 1799, a man named Napoleon Bonaparte was elected the First Consul of the Consulate in France. It wasn't until May of 1804 that that same man was declared emperor by the Senate. He was crowned on December 2 of that very same year. This began a long and tumultuous reign. Starting in 1806, he began appointing his relatives as high officials to gain power, starting with declaring his brother, Joseph Bonaparte, King of Naples. After that it pretty much spiraled down even more. In 1806 Prussia joined Britain and Russia against Napoleon. After that, many battles are fought, and it wasn't until 1814 that Napoleon abdicates his rule in favor of Louis XVIII. Oddly enough, that was not the end of Napoleon's life. He left for Antibes after slipping away from Elba and on March 20, 1815, arrived back in Paris. After that the United Kingdom, Russia, Austria and Prussia put together 150,000 men to defeat Napoleon once and for all. More battles were fought, and the Neapolitans signed a treaty with Austria in the meantime. On June 18, 1815, the famous battle of Waterloo was fought. It was very close, but in the end the combined armies of Wellington and Blücher defeated Napoleon's army. That was the beginning of Napoleon's downfall. Just four days later Napoleon abdicated, but he didn't just hand over the throne--he gave it to his son, Napoléon II. The 1oo days between his escape from Elba and his defeat in battle at Waterloo ended the Napoleonic Era and brought Louis XVIII and monarchy back to power in France.