OK, so Hamlet comes back from undergrad, his uncle has poured poison in Dad’s ear and married Mom. (Should I have used a spoiler box?)
So the King is dead. Why isn’t Hamlet king?
Because Claudius politicked his way into the throne. This was made easier for him because:
(1) Hamlet was away in Germany;
(2) Claudius married the former queen.
It’s not all that different from the way that Richard III became King of England, and Shakespeare wrote a play giving some of the details of that.
I read a discussion of this in Asimov’s Guide to Shakespeare. In early Medieval* Europe, succession did not always fall automatically on the king’s eldest son, but sometimes by “election” (of the leading nobles) on the likeliest male of the royal family. This avoided the problem (which emerged later in some kingdoms) of the king being a child or an idiot. In Hamlet’s case, his father died while he himself was away at a university in Germany – while his uncle (who apparently timed it so) was there in Denmark, in a position to press his claim and make it stick, and cement it by marrying the royal widow. That is why Hamlet is so resentful, even before his father’s ghost visits him. Asimov also points out that based on internal evidence, Hamlet does not appear to be a mere callow freshman or sophomore, but a man in his mid-to-late '20s, so he could have had a fair shot at the election if he had been in Denmark at the time; which adds to his resentment.
*Shakespeare wrote the play in a more-or-less Sixteenth-Century milieu – Claudius has a guard of Swiss mercenaries, like many kings of Shakespeare’s time, and Hamlet is a Renaissance prince with all the “new learning” at his fingertips – but the origins of the Hamlet legend are much older.
Likewise, in Macbeth, Macbeth, although not the king’s son, is able to make a credible claim for election to the throne after he murders the king and frames his son for it. (The story of the historical Macbeth’s succession is less villainous.)
What **BrainGlutton ** said. Plus, let’s not forget it was a bit of a wartime emergency - Young Fortinbras is nipping at Denmark and a strong presence at the head of the state was needed. Even so, foreign support was slow in coming (When Claudius sends Hamlet to his death in England, he mentions it’s in lieu of England’s neglected tribute), and a lot of confusion surrounding the monarchy would have made things worse. You can’t look weak or indecisive (the irony…it burns!).
There’s this passage in Act V which suggests the Danish throne was elective within the royal family:
Asimov also points out that the story is not a mere family quarrel and nothing about it would make sense if the characters were not royalty. Hamlet does not just want revenge for his father, he wants to be king, and that constrains how he can act and under what circumstances he can safely kill Claudius; it also makes his life very dangerous, because he knows Claudius is carefully watching him for any sign of movement and any pretext to get rid of him. It’s not really the “tragedy of indecision.” Hamlet is not indecisive, he is constrained and frustrated by circumstances.
And this was in fact the case until 1665, when hereditary primogeniture was established by law. Hamlet was written around 1601.
And, of course, Hamlet’s final lines:
Ham. O, I die, Horatio!
The potent poison quite o’ercrows my spirit.
I cannot live to hear the news from England,
But I do prophesy th’ election lights
On Fortinbras. He has my dying voice.
So tell him, with th’ occurrents, more and less,
Which have solicited- the rest is silence.
And the story’s origins go back at least to the 13th century, when Saxo Grammaticus discussed it in the Gesta Danorum.