Just an extended metaphor for syphilis...

A (not so) Brief Rundown:
Act 1: It's the highly symbolic changing of the guard, and in that time of night a ghost appears to two guards and their friend Horatio, who was there because he wouldn't believe the ghost existed until he saw it with his own eyes. After the ghost vanishes, they have a long discussion about the socio-political happenings of the area to get the audience up to speed, and we learn about Old Hamlet and Old Fortinbras, and young Fortinbras' bid to take back the land his father lost. There's a lot of foreshadowing, and they decide to tell young Hamlet about the ghost. Then we see Claudius and Gertrude, being happy and carefree, and we see Hamlet raining on everyone's parade. When everyone leaves, he talks a lot about how much his life sucks and how his mother is a whore, et cetera, until his old friend Horatio shows up and tells him about the ghost. Hamlet agrees to go see it that night. Then, we cut to a different family-- Polonius' children, Laertes and Ophelia. Laertes is going on a long journey back to school in France, and he reminds Ophelia not to sleep with Hamlet. Then Polonius gives the 'never a borrower' speech, and bids Laertes farewell. When Laertes leaves, Polonius tells Ophelia not to sleep with Hamlet, and goes even farther, telling her to refuse to see him. Then, finally, we see Hamlet with the guards, and the ghost appears. He follows it, and it explains that Claudius killed it and asks Hamlet to enact his revenge. When the guards catch up to them, Hamlet makes them swear to secrecy not to reveal his plan to act crazy. For some reason.

Act 2: We open with Polonius instructing his servant to spy on his son in an incredibly roundabout manner, casting doubt on the healthiness of their family's relationship. Then Ophelia runs in, talking about Hamlet running into her closet and acting crazy. Polonius decides that this is because Hamlet is crazy with love, and resolves to tell the King and Queen about it. When we see the King and Queen, they are speaking to Rozencrantz and Guildenstern, who they instruct to spy on Hamlet to see what has disturbed him. They depart, and Polonius enters, with his news. Before Polonius can say anything, Voltimand returns with word from Norway, Fortinbras' uncle-- who has successfully stopped Fortinbras from invading Denmark, instead sending him to Poland. This point settled, Polonius shares his news about Hamlet's supposed lovesickness, reads one of his letters to Ophelia aloud, and insists that they spy on Hamlet and Ophelia together. Hamlet arrives, and he and Polonius have a loaded exchange, and Polonius departs defeated. Then it is Rozencrantz and Guildensterns' turn to take a crack at figuring out Hamlet, but Hamlet senses that they aren't working out of kindness, and shuts them out. Then, the players enter, bringing with them a whole host of symbolism. Hamlet jests with them, gives a monologue, and is given a monologue in return. When everyone leaves, Hamlet has a massive monologue where we learn he intends to tell if Claudius is guilty based on Claudius' reaction to the play.

Act 3: This begins with Rozencrantz and Guildenstern discussing Hamlet's actions with the king and queen. All but the King, Polonius, and Ophelia leave, and they set their trap for Hamlet to see if love is truly behind his madness. Hamlet enters with his famous "to be or not to be" speech, and he and Ophelia fight instead of make up. When it's clear that love is not behind Hamlet's madness, Polonius recommends that Gertrude should talk to Hamlet, to see if she can figure out what's wrong. Claudius agrees. Then we see Hamlet rehearsing with the players, bossing them around right before the show. Rozencrantz, Guildenstern, and Horatio show up. Hamlet tells Horatio to watch the king for signs of guilt. Everyone else files in, Hamlet rather aggressively flirts with Ophelia, and then the play begins. The play is basically the backstory to Hamlet: Brother kills king, takes his wife, &c. Then a dialogue between a dying king and his loving wife. Finally, as Lucianus (a character in the play within a play) pours poison into his brother's ear, the King gets fed up and leaves. Hamlet and Horatio determine the king's guilt, Hamlet yells at Rosencrantz and Guildenstern when they come to summon him to his mother. It is only when Polonius summons him, that Hamlet consents to go. He dismisses everyone, and has another monologue. In his own room, the King speaks to Rozencrantz and Guildenstern, and decides to send Hamlet away with them to England. Polonius enters, reminds the King that Hamlet will talk to Gertrude, and exits, and the King is left alone to monologue about his own guilt and corrupted soul. Hamlet sneaks in as Claudius begins praying, but decides not to kill him, instead going in to talk to his mother. They fight, Hamlet kills Polonius, they fight some more, the ghost shows up,  and then Hamlet leaves.

Act 4: Gertrude reports to the King that Hamlet is truly nuts, that he killed Polonius, and the King reassures her that he's sending him away. He sends Rozencrantz and Guildenstern to go apprehend Hamlet, they return with him, and the King interrogates him. He is sent to board a ship, and when he gets to the docks, he meets Fortinbras, his very own foil. Fortinbras' men are off to claim some podunk chunk of Poland, and this pointless act of war inspires Hamlet to be a man of action. Back in Elsinore, Ophelia goes crazy, sings her loaded songs about pregnancy and betrayal. A messenger runs by with the news that Laertes has heard of Polonius' death, and, blaming Claudius, has begun a revolution. He storms in, threatening the King's life, and is slowly calmed down when he learns that Claudius wasn't Polonius' murderer. Ophelia enters again, bestowing flowers to all around, and breaking Laertes' heart. Then Horatio gets the news about Hamlet and the *~*~magical plot device pirates~*~* and goes to bring him back. As Horatio leaves, the King and Laertes discuss what Hamlet's fate was meant to have been when word comes that Hamlet yet lives. They hatch a plan to kill him, with a poison blade during an innocuous duel. Then Gertrude enters, with news of Ophelia's death-by-drowning.

Act 5: Two grave diggers discuss the socio-political reasons for Ophelia being buried in the church despite her suicide. Hamlet talks about dead kings and reminisces about poor Yorick. Ophelia is buried, and Laertes and Hamlet get into a fight about who mourns her more. Back in Elsinore, Hamlet and Horatio talk, Hamlet is summoned to the duel, and he makes his peace with death, much to Horatio's dismay. The duel with Horatio begins, and quickly gets out of hand as Claudius poisons a glass of wine as a plan B. Gertrude drinks the wine, both Hamlet and Horatio are cut with the poison blade, and Hamlet forces Claudius to drink his own poison. Horatio himself almost kills himself at the end, but is stopped by Hamlet. In the end, Fortinbras, who is simply passing through, is given the throne of Denmark, and gives Hamlet a soldier's funeral.

An actually brief character analysis:
Hamlet: Our protagonist, the possibly-crazy Prince of Denmark. He's a thinker not a doer, and it is made clear that we see him at the low end of his life. Prior to having his life apparently ruined, he was a scholar, and he is unsuited to the fate given to him. Still very much a child.

Claudius: A murderer, but not a happy one. He killed his brother for the throne, and for the right to marry Gertrude. but life is not all roses for him, especially once Hamlet begins to track him down.

Gertrude: Hamlet's mother. She's not as easy to pin down, because her character depends largely on acting choices. It seems at least that she still loves her son, but she did not hesitate to marry Claudius.

Ophelia: Hamlet's girlfriend of old. She goes insane (maybe) when her father Polonius dies, and it is heavily insinuated that she is pregnant, and Hamlet is the father. Her life is basically ruined when Hamlet goes crazy, and she drowns herself in the end.

Laertes: Ophelia's brother. Ends up killing Hamlet, with a poisoned blade, in order to take revenge of his father's death and his sister's suicide, but regrets it in the end and exposes the King as a traitor.

Horatio: The one true friend that Hamlet has left at the end. He's stable and unwilling to believe things he hasn't seen himself. He is one of the only characters left alive at the end of the play, and shares Hamlet's story with Fortinbras. He is probably dating Hamlet. 

Style
     The thing about discussing Shakespeare's style is that most of it has already been said (iambic pentameter rhyming couplets extended metaphors and time-specific political jokes, essentially). Within the actual content of his extended metaphors and rhyming couplets, however, there are a lot of recurring ideas. An image that often gets thrown around is the idea of the ear; characters are frequently told to listen, Hamlet calls Claudius a blistered ear, ect, to remind the reader of the cause of King Hamlet's death. Similarly, there is a lot of language with connotations of rot and decay, corruption and filth, and so forth. From the moment it is declared that 'something is rotten in the state of Denmark,' no one can drop the idea of decay and filth. Hamlet is especially fond of discussing weakness and corruption. He also frequently uses pregnancy words, references conception, and expresses disdain towards Ophelia for her interest in him. All that contributes to the idea that the entire royal house, and by extension the kingdom itself, is corrupted beyond repair.
     There are very few objects actually denoted in Hamlet for characters to have, another problem with discussing Shakespeare. Many directors, though, picking up on textual clues, litter the sets with mirrors-- because Hamlet has trouble discerning what is real. They are an added symbol, but a fitting one nonetheless. The four elements, however, are frequently referenced, particularly water, standing in for  madness. When Ophelia drowns herself after going crazy, Laertes remarked that she had too much water. Gertrude describes Hamlet's insanity as being similar to the air meeting the ocean. Snakes are another subtle symbol-- King Hamlet was purportedly killed by a snake, who was in reality Claudius. Hamlet relates Rosencrantz and Guildenstern to adders. Snakes are an oblique reference to the devil, and especially with King Hamlet's death in a garden, the image contributes to an idea of a fallen Paradise, that has been, as the diction I mentioned earlier indicates, hopelessly corrupted.
     Keeping all of this in mind, the tone of Hamlet isn't about to set you skipping. The whole play is intensely fatalistic, Horatio dropping approximately 4 'this is foreshadowing' words in the first scene of the entire thing. Hamlet, too, insists that his destiny calls him when he goes to confront the ghost, and his belief in fate carries through to the very end when he makes his peace with death, claiming that even if it isn't going to happen now, it will happen eventually. Everything contributes to give a general feeling that nothing could have been prevented, no matter what was changed, and Hamlet's insistence on the horrors of the world around him cast a gloom over the play regardless of whether or not the reader gives him credence.

Quotes:

• Hamlet: "Seems, madam! Nay, it is; I know not "seems." 'Tis not alone my inky cloak, good mother, nor customary suits of solemn black. . . That can denote me truly: these indeed seem, For they are actions that a man might play." 

          As I have mentioned, Hamlet is horrible at distinguishing what is real from what is represented, and he has an even worse time understanding that sometimes those two things are one and the same. A lot of what makes him suspect those around him (even if his suspicion is not reasonless) is his inability to accept anyone's outward displays of emotion. Although he vouches for the veracity of his own sorrow in this quote, he also informs us all that people certainly can and do fake emotions, which is a big freaking clue that he won't trust those around him. 

• Hamlet: "Alexander died, Alexander was buried, Alexander returneth into dust; the dust is earth; of earth we make loam; and why of that loam, whereto he was converted, might they not stop a beer-barrel?"

           We get a couple interesting tidbits here. This involves Hamlet discussing the fate of great kings, and subconsciously the fate of his father, who he knows to be walking in Purgatory. Alongside the subconscious fear and possible revulsion Hamlet truly has for his father, Alexander's less-than-great fate is explained. It also tips a hat to Hamlet's religious bent, referencing the 'from dust we came, and to dust we shall return' factor of religion. Since the play could be considered Hamlet's long long journey to acceptance of his own death, this commentary on the transience of greatness (the journey from a conqueror to a beer-bottle stopper) is definitely a step in the process. What is the point of conquering and earning greatness if all that is left of you on Earth will end up with a menial fate? 

• Ophelia: "Methinks this imparts the meaning of the play"

          I will never get tired of talking about how meta Hamlet is, because it is so very, very meta. This line, dropped as it is while the characters we are watching in a play watch other characters in a play that were crafted to be a deliberate echo of the characters that we also recognize as characters, is almost a subtle hint that the people we are watching are semi aware of their role. Hamlet drops constant hints in his dialogue about acting, putting on plays, about art and pictures and there's a moment when talking to the players where he instructs them to be more lifelike, which is a very odd scene to put into a play itself. This, however, is the one specific quote that provides the biggest hint towards the fourth wall breaking nature of Hamlet as a play. 

Theme:

Hamlet is a play about the inevitability of decay.

     When we first hear Hamlet explain that he is going to pretend to be crazy, we all cringe, because we know what's coming next. He's actually going to go crazy, we assume. Either way, from the moment he says that, we know we can no longer trust him completely. Is he fully in control? Or is he just hiding his madness behind the veneer of acting again? This sort of spiral from bad to worse is a common occurrence in the play. From the bad of Claudius poisoning his brother, to the worse of the decay of the state of Denmark and the widespread death of the royal house. From the bad of Polonius' discovery of Ophelia and Hamlet to the worse of Ophelia going mad with despair and killing herself. From the bad of the vague threat of Fortinbras' takeover, to the worse of his eventual control over the kingdom, every single threat that appears to hold water in the beginning of the play simply spirals out of control. 

     Hamlet also likes to talk about death, about how since death is inevitable life is meaningless, about how Cesar and Alexander, great kings though they may have been, are now dead and dust. This entrenched fatalistic idea Hamlet carries goes far to explain his own inaction. Why kill Claudius and damn his immortal soul if his soul is all that he truly has left to cherish? Why become a king, why conquer a land,  why bother continually screwing over Poland, if they can be lost upon your death and granted to your enemy? His priorities have always been set with his death in mind, and he courts death almost from his introduction as a character. He 'does not set his life at a pin's fee' one moment, affirms that only fear prevents suicide the next. Truly, Hamlet never wanted to live, so he sees no reason to devote himself to life when he knows that death is inevitable.

     In terms of actual devices, Shakespeare leans very heavily on the foreshadowing stick in this case. From Horatio's friendly reminder about the ghosts that rose in Rome before it's fall, echoing not only the idea that Denmark will fall, but providing a hint to Horatio's insistence that he is 'more an antique Roman than a Dane' to the initial threat of Fortinbras' takeover, Shakespeare warns his characters quite clearly what is about to befall them. The constant mentions of poison, rot, undesirable pregnancy, and elemental madness also contribute to the inevitability and their persistence aids in the feeling of a constant downward spiral. 

Again, this is not a happy play.