What are the internal and external conflicts in Act 1 of Hamlet?

There is also a conflict between Hamlet and his mother, as she seems to expect him to be out of mourning, though his father only recently died.  She tells him to,

 Cast thy nighted color off,
And let thine eye look like a friend on Denmark.
Do not forever with thy vailed lids
Seek for thy noble father in the dust. (1.2.70-74)

Gertrude wants Hamlet to cheer up and quit dwelling on his father's death.  This angers Hamlet because, as he says, "I have that within which passes show / These but the trappings and the suits of woe" (1.2.88-89).  In other words, he feels the loss of his father deeply, and he does not just wear mourning clothes for "show." This implies that this is what his mother has done.

There is additional conflict between Hamlet and his stepfather/uncle Claudius, both the new king and his mother's new husband.  Hamlet has requested permission to return to school in Wittenberg, but Claudius denies him, saying, 

Your intent 
In going back to school in Wittenburg,
It is most retrograde to our desire,
And we beseech you, bend you to remain
Here in the cheer and comfort of our eye. (1.2.116-120)

Claudius implies that he wishes to keep Hamlet at home, in Denmark, because the king cares so deeply for his new "son."  It is more likely, however, that Claudius wants to keep an eye on Hamlet because the prince is acting strangely.  We can contrast his refusal of Hamlet's request with his acquiescence to Laertes's request to return to France; Claudius seems a lot more familiar and comfortable with Polonius's son than his own nephew.

The first, and main, external conflict of Hamlet is the conflict that exists between Claudius and Hamlet.  In Act I, the external conflict is a bit one sided thought.  Hamlet suspects that Claudius murdered his father, so Hamlet wants revenge, but Claudius doesn't know this.  It's not an external conflict full of fisticuffs and sword fights until later.  

The internal conflict is squarely centered on Hamlet.  There are actually several.  First, Hamlet struggles with communicating with ghosts.  

If it assume my noble father's person, 
I'll speak to it, though hell itself should gape 
And bid me hold my peace

He wants the information that the ghost has, but Hamlet does worry about his eternal soul.  

Another internal conflict of Hamlet's is his love and relationship with his mother.  She's his mom.  He loves her, but he struggles with how he feels about her after knowing her actions with Claudius.  

The last internal conflict that is introduced in Act I is Hamlet's struggle with revenge and death.  He knows murder is wrong, but wants revenge.  He also is so distraught that he struggles with his own will to live while knowing that he should be seeking vengeance.  This last conflict will continue to grow throughout the rest of the play.  

Hamlet is a play filled with conflicts, both internal and external. To get started answering this question, let's review some of them. One of the central conflicts of the play is a murder mystery. The ghost of Hamlet's father claims that his brother, Claudius, murdered him and stole his crown. Indeed, Claudius has married Hamlet's mother, Gertrude, and has become the new king.

Hamlet is left to decide what to do about this. He has been grieving deeply for his father, yet part of him doubts the ghost, and he hesitates to act, berating himself in the process. Herein lies one of Hamlet's major internal conflicts. He must decide whether or not to take revenge upon his father's murderer, and he must discover some incontrovertible proof before he can fully make up his mind. When the players arrive at the castle, Hamlet develops his plan. He will have the players act out a murder and watch Claudius's reaction. The plot moves along quickly from here, and the play is, indeed, the thing that catches the king.

Hamlet, however, isn't the only character experiencing conflicts. Gertrude herself struggles internally because of the external events of the play. She has indeed married her husband's brother, but Hamlet has made her realize the repulsiveness of her actions, and she regrets what she has done. She also struggles to see her son apparently go crazy before her eyes, even though Hamlet assures her he is only pretending to be mad.

Ophelia, too, experiences severe internal conflicts because of what has happened. Hamlet appears to be crazy and is now spurning her, yet she is still deeply in love with him. Her father and her brother are pushing her into helping them discover what is going on with Hamlet, and she obeys. She is pulled in many different directions at once, and her fragile psyche cannot handle it. Ophelia goes mad for real and commits suicide.

Even Claudius is struggling internally on some level. If he had no guilt, he would not react so strongly to the play. Deep down, he knows his crime, and when he sees it enacted before him, he calls for light and runs out. The plot continues to move forward, for now Claudius wants Hamlet dead.

In Hamlet, what are Hamlet's external and internal conflicts?

When Hamlet first appears in act 1, scene 2 of Shakespeare's Hamlet, he's obviously troubled, but it's not until his rambling soliloquy midway through the scene that the audience is made aware of what is truly troubling him.

Hamlet makes it clear in the earlier part of the scene that he's grieving his father's death. Hamlet's uncle, Claudius (now king), and his mother, Gertrude (now married to Claudius), aren't happy with the extent to which Hamlet is displaying his grief, but Hamlet pretty much ignores them about that.

Claudius and Gertrude ask Hamlet to stay in Denmark rather than return to school in Wittenberg—Claudius wants to keep an eye on Hamlet, and Gertrude simply misses him—and Hamlet acquiesces to their request without objection.

What's clear, too, is that Hamlet doesn't like his uncle, although the nature of the conflict isn't made clear until Hamlet's soliloquy.

In his soliloquy, Hamlet starts with the usual questioning of his existence—essentially, "why was I born, and maybe I should just kill myself"—which he revisits periodically during the play, but the primary focus of the soliloquy is what Hamlet perceives as his mother's "incestuous" marriage to Claudius. Hamlet might not have liked Claudius very much anyway, but Claudius's marriage to his mother simply exacerbates any ill feelings that Hamlet has for Claudius.

Hamlet's soliloquy shows, however, that even though he dislikes Claudius, at that point in the play Hamlet is more upset with his mother and that he holds his mother more responsible than Claudius for the marriage. Hamlet knows that he can't do anything about the marriage, and he decides to keep his thoughts and feelings about his mother to himself.

HAMLET. It is not, nor it cannot come to, good.
But break, my heart, for I must hold my tongue! (act 1, scene 2, lines 161–162)

Once the ghost of Hamlet's father tells Hamlet that Claudius murdered him, however, Hamlet's conflict with Claudius intensifies and becomes the focus of his existence, while Hamlet's conflict with his mother seems to dissipate entirely.

The inner conflict for Hamlet is not "To be, or not to be"—because he already decided not to kill himself in the first soliloquy—but "should I or shouldn't I?" Should he avenge his father's murder by killing Claudius or not? Hamlet's external conflict with Claudius, that he basically doesn't like him, becomes Hamlet's inner conflict because he vows to avenge his father's death.

Hamlet resolves this conflict by finding reasons to do nothing. He questions the veracity of the ghost and decides he needs more proof of Claudius's guilt.

HAMLET. The spirit that I have seen
May be a devil; and the devil hath power
T' assume a pleasing shape; yea, and perhaps
Out of my weakness and my melancholy,
As he is very potent with such spirits,
Abuses me to damn me. I'll have grounds
More relative than this. The play's the thing
Wherein I'll catch the conscience of the King. (act 2, scene 2, lines 593–600)

Hamlet has a perfect opportunity to kill Claudius while he's praying, but the fact that Claudius is praying gives Hamlet a perfect excuse not to kill him.

HAMLET. Now might I do it pat, now he is praying;
And now I'll do't. And so he goes to heaven,
And so am I revenged. That would be scann'd.
A villain kills my father; and for that,
I, his sole son, do this same villain send
To heaven.
O, this is hire and salary, not revenge! (act 3, scene 3, lines 76–81)

Hamlet's external and internal conflicts with Claudius are resolved concurrently at the end of the play but by the circumstances of the moment, not by Hamlet's intentional fulfillment of his vow to avenge his father's death. Hamlet is overwhelmed by emotion at his mother's death and his own impending death, and Hamlet strikes out at Claudius, killing him.

Discuss Hamlet's internal and external conflicts.

A list of Hamlet's external conflicts is relatively easy to generate.  He has conflicts of some sort with nearly every character on the list except his good friend, Horatio.  The internal conflicts are a bit more complex and subtle.

Here is quick list of what is creating his conflict with each of the characters.  You can find quotes to illustrate the conflict by reviewing the scenes where those characters interact with Hamlet.

• Claudius -- the man who killed Hamlet's father and very quickly married his mother, making his uncle his father.  Hamlet is very disgusted by the marriage and finding out the truth of the murder from the ghost makes them mortal enemies.
• Gertrude -- his mother's quick remarriage to Hamlet's uncle is appalling to Hamlet's sense of morality and dignity.  He eventually confronts her with what he perceives to be all her wrongdoings at the end of Act 3.
• Rosencrantz and Guildenstern -- his supposed childhood friends who are only at court at the request of the King and are actually serving as spies for Claudius.  Even when they are confronted about their motives, they lie to Hamlet.
• Polonius -- courtier to King Claudius and father to Ophelia, he is always trying to spy on Hamlet and he has so little faith in Hamlet that he commands his daughter to break things off with Hamlet.
• Ophelia -- the girlfriend of Hamlet who breaks up with him because her father tells her to.  Later she seems to betray Hamlet by lying to him about where her father is when Hamlet suspects that he is actually spying on their conversation.
• King Hamlet -- his arrival as a ghost who then tells the story of how Claudius murdered him is both awful and dangerous.  Hamlet knows that ghosts may only be the devil in the disguise of a loved one who is trying to damn his soul, so he must prove that the ghost is telling the truth.
• Laertes -- after Hamlet accidentally kills Polonius, Laertes' father, Laertes is out for vengeance and plots together with Claudius to bring about the death of Hamlet in a fixed sword fight.

As for his internal conflicts:

• Hamlet is torn between thoughts of suicide and God's commands against such an act.
• Hamlet wants to fulfill his father's command for justice yet has a hard time acting swiftly because he feels he must have proof.
• Hamlet is torn between thinking and action.  The "To be or not be soliloquy" is essential to this point, but it is a theme that runs throughout the play.
• Hamlet wants to think he can control everything in his life, but comes to realize that all he really do is be ready -- "the readiness is all."

In Shakespeare's Hamlet, which characters face both internal and external conflict?

Everything written is as good as it is dramatic. It need not declare itself in form, but it is drama or nothing.                                                  - Robert Frost

Drama is based on conflict. Conflict creates problems for one or more characters, and we tend to emphasize with one character, such as Hamlet, because of his problem and not because of his character. This empathy is a natural part of human nature. We are psychologically and emotionally programmed to want to help other people if they are in trouble. Some people take advantage of this natural human tendency. Panhandlers are a good example. But there are many others, including all those people who call us on the phone and ask us to contribute to some organization which is probably running a scam out of a "boiler room."

In Shakespeare's Hamlet, there are only two characters who face both internal and external conflicts. These are, quite appropriately, Hamlet and Claudius. Hamlet is engaged in an ongoing psychological conflict with Claudius and at the same time fighting an internal conflict between his duty to revenge his father and his reluctance to commit murder and regicide. Claudius, for his part, is afraid of Hamlet because the younger man is not only the rightful heir to the throne, but he is infinitely better educated and more intelligent than the crafty, cunning King. At the same time, Claudius is eaten up with guilt because of the terrible crime he has committed, as he reveals in his futile attempt to pray and elsewhere in asides. Some famous psychologist, probably Freud, said that guilt is nothing but fear of punishment; so Claudius is suffering from fear which he takes pains to hide from everyone. His heavy drinking is not for pleasure but to deaden his memories and his internal panic. He would really be panicked if he knew that Hamlet had been talking to his father's ghost and knew all about his wickedness.

When two characters are involved in a conflict, there should be something tangible that the conflict is about. This used to be called the "bone of contention." In Hollywood parlance it is called the "MacGuffin." In Hamlet the MacGuffin can only be the royal crown. Claudius wants to keep it. Hamlet knows that he could obtain it if he handled the situation adroitly. He is the legitimate heir. The people love him. Polonius would certainly be on his side because the old man would love to have Hamlet marry Ophelia and make his daughter queen. But if Hamlet simply murders Claudius, that could seriously hurt his chances of being elected the new king. What he needs to do is to expose Claudius as the murderer and usurper-- and then kill him.

Claudius is terribly suspicious of Hamlet. He keeps him a virtual prisoner at Elsinore and spies on him, trying to find out if his nephew is plotting against him. He uses Polonius, Ophelia, Rosencrantz, Guildenstern, Gertrude, and no doubt many servants and courtiers to spy on Hamlet and report to him. In one of Shakespeare's most beautiful metaphors Claudius says of Hamlet:

There's something in his soul,
O'er which his melancholy sits on brood,
And I do doubt the hatch and the disclose
Will be some danger

In the conflict between Claudius and Hamlet, we naturally empathize with Hamlet because we know Claudius to be a murderer and a villain. But Hamlet has huge, complicated internal and external problems. This is how Shakespeare gets us involved in the drama. We are hoping to see Hamlet win and Claudius lose.