1.1: We hear from Canterbury and Ely that Henry is thinking about invading France so he can take the French throne by force.
1.2: Henry is convinced (by Canterbury) that he has a legal right to the French crown because he's the great-great grandson of Isabella, who was the daughter of the French King Phillip IV.
1.2: Henry receives the Dauphin's insulting gift (a chest full of tennis balls) and sends word to France that he's going to invade the country with his army.
2.2: Henry has learned about a plot to assassinate him. He confronts the three traitors (Cambridge, Scrope, and Gray) and sentences them to death. Then he hops on a boat and heads across the English Channel to invade France.
2.4: Henry sends a message to King Charles of France that goes something like this: "Dear Charlie, I've arrived in Harfleur so you better give up your crown ASAP. Otherwise, we'll have to go to war and it will be your fault when my army turns your women and children into widows and orphans. Your pal, Harry."
3.1: Henry attacks the town of Harfleur after rallying his troops with a famous battle cry: "Once more into the breach dear friends, once more!"
3.3: Henry convinces the Governor of Harfleur to surrender after threatening that his English soldiers would probably rape and massacre his people if the town didn't submit peacefully.
3.6: When Henry finds out that his old pal Bardolph has been sentenced to death for looting a French Church, he says Bardolph is getting what he deserves and that anyone else caught looting will get the same.
3.6: King Henry responds to a threat from Charles. Henry admits that his troops are down and out, but says that they'll fight to the death before they give up. Henry says it's "in God's hand."
4.1: The night before the Battle of Agincourt, Henry walks around the English camp cheering up his troops.
4.1: Henry disguises himself as a commoner and roams around the camp talking to his soldiers. He argues with Williams about whether or not it will be the king's fault when English soldiers are slaughtered in battle.
4.1: Henry delivers a speech about the difficulties of kingship. Being his country's leader has left him feeling isolated and exhausted. He prays that God will forgive him for his father's sins (usurping the crown from Richard II).
4.3: Before heading into battle, Henry delivers a famous motivational speech to his troops, urging them to fight for honor. He tells his men that warfare has made them like a family: "We few, we happy few, we band of brothers. / For he today that sheds his blood with me / Shall be my brother."
4.3-4.7: Henry and his army defeat the French.
4.7-4.8: Henry plays a trick on Williams and Fluellen.
5.0: We learn from the Chorus that Henry returns to England, where they throw a big parade for their victorious king. Soon after, Henry goes back to France to take care of unfinished business.
5.2: Henry goes to the French palace and signs a peace treaty that will make him 1) the heir apparent of France and 2) Catherine's new husband.
5.2: Henry proceeds to woo Catherine, even though he knows she has no choice but to marry him.