King Henry IV is Prince Hal's father and the title character of Shakespeare's play. Throughout the play, Henry's reign is threatened by border skirmishes with the Welsh and Scots, a rebel uprising, and a rocky relationship with his seemingly degenerate kid, who stands to inherit the throne.
When we first see King Henry, the poor guy's exhausted. He tells us he's "shaken" and "wan with care" from his reign's tumultuous beginnings. And, even though he doesn't come out and say so, we know he's feeling seriously guilty about his past. In the play that precedes Henry IV Part 1 (Richard II ), Henry stole the throne from King Richard II and then ordered Richard's murder, accidentally, sort of. Because kings were seen as God's divinely appointed rulers on earth, Henry believes his actions are an affront to God, which is why he's so eager to lead a united English army on a Holy War in Jerusalem (1.1.1). All in all, the guy's got some serious baggage and his revolt against King Richard II has basically paved the way for the Percy family's uprising.
As a usurper whose got no blood claim to the throne (the crown typically passes down from fathers to sons), Henry's got to figure out a way to maintain power. The king's problems raise important questions about authority and rebellion: How can one be an effective ruler when his own rebellious past seems to have opened the door for future uprisings? Can rebellion against the monarch ever be justified? We talk about these issues in more detail in "Power" and "Rules and Order," so be sure to check out "Quotes" for these themes.
Because Prince Hal is poised to inherit the throne by lineal succession, Henry's tumultuous relationship with his son is nearly inseparable from matters of state. Henry worries about Hal's fitness to govern after his death and often laments that he's the father of such a rotten kid (1.1.4). He also feels that God has sent Prince Hal to earth as a personal form of punishment for Henry's sins against King Richard II (3.2.1). In fact, Henry frequently comments that he wishes Hotspur were his son and that fairies had exchanged Hal and Hotspur at birth – according to Henry, the young Percy would be a terrific king (1.1.4). See what we mean when we say Henry can't separate being a dad from being a king?
This is a pretty brutal attitude, but it allows Shakespeare to meditate on the similarities between kingship and parenting, a point that's never lost in a play that imagines civil warfare as a kind of large scale family squabble. Shakespeare also seems to be interested in the way Henry's relationship with his son dramatizes some common issues surrounding primogeniture (the system by which eldest sons inherit their fathers' wealth, titles, lands, power, debt, etc.). When Henry reveals he's been afraid that Hal wants to see him dead so he can be king (5.4.5), Henry gives voice to an anxiety that all sons look forward to their fathers' deaths. The play's concerns with Henry and Hal's familial bond links Henry IV Part 1 with other plays concerned with father-son relationships (most notably, Hamlet and King Lear).