Don't let the name fool you: Henry IV, Part II, is actually about Henry V, then Prince Henry. He transforms from an irresponsible youth to a proud and upstanding King, presumably from the death of his father.
I once heard an author talking about George Bush as a Henry V, trying to expand upon his father's name. I'll explore that in the post on Henry V proper, unless I forget to.
Some good quotes:
Rumour: "They bring smooth comforts false, worse than true wrongs."
Falstaff: "I am not only witty in myself, but the cause that wit is in other men" ie. not only am I good at making jokes, but people make good jokes about me too.
King Henry: "Uneasy lies the head that wears the crown." This line is part of a larger speech in act III, scene I. It and the other speech in the same scene are fantastic.
Prince Henry: "Oh, majesty! When thou dost pinch thy bearer, thou dost sit like a rich armour worn in heat of day, that scalds with safety."
In fact, all of Act IV, Scene IV, is good.
Act III, Scene II has a goofy scene where Falstaff interviews men to serve as soldiers and makes puns on their names. Shakespeare must have had some sort of pun fetish.
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Next Up: King Henry V
I've been reading a little of Henry V, and it's good. One speech has two very good quotes. More later.