For this relief much thanks. 'Tis bitter cold,
And I am sick at heart.
 

Hamlet opens at night as Barnardo, a watchman guarding the castle at Elsinore, relieves another watchman, Francisco, who is at the end of his shift. This quote by Francisco might sound like an off-handed comment, but it represents more when its context is fully considered. The castle at Elsinore stands as a vast bulwark to prevent the invasion of Denmark by foreign enemies, who are a constant threat. Therefore, the guardsmen are symbolically protecting not just the castle, but the entire Danish state. By stating that it is bitterly cold out and that he is “sick at heart” (depressed), Francisco is conveying to the audience that these are troubling times in Denmark.

The same sentiment will be more memorably expressed later (in Act 1, Scene 4) by another guardsman, Marcellus, when he famously says, “Something is rotten in the state of Denmark,” but the play’s theme of The Ill Health of the State (the sixth theme) is first hinted here, less than ten lines into its first scene.

What art thou that usurp’st this time of night
Together with that fair and warlike form
In which the majesty of buried Denmark
Did sometimes march? By heaven, I charge thee, speak.

Hamlet takes place entirely in or around the castle fortress at Elsinore in Denmark except for one brief scene. The ominous atmosphere of this setting is fixed in the play’s first scene when the Ghost of the recently deceased King Hamlet appears and is confronted by Prince Hamlet’s friend, Horatio. The dynamics of this quote and its significance is further explained in Quotes by Setting: Elsinore, Denmark (the first quote).

In what particular thought to work I know not,
But in the gross and scope of mine opinion
This bodes some strange eruption to our state.

This is another quote from Horatio’s encounter with the Ghost in Act 1, Scene 1. Horatio, a scholarly friend of Prince Hamlet, has been invited by the castle watchmen Marcellus and Bernardo to witness a recurring apparition that reveals itself outside the castle at Elsinore. The apparition, a ghost, appears as the three are standing in the dark. Here, using characteristic clear-headed language, Horatio agrees with the watchmen that the Ghost resembles the recently deceased King Hamlet, and says that while he cannot explain the apparition, he believes that it represents bad news for the state of Denmark.

At least, the whisper goes so: our last king,
Whose image even but now appeared to us,
Was, as you know, by Fortinbras of Norway,
Thereto pricked on by a most emulate pride,
Dared to the combat; in which our valiant Hamlet
(For so this side of our known world esteemed him)
Did slay this Fortinbras, who by a sealed compact
Well ratified by law and heraldry,
Did forfeit, with his life, all those his lands. . .
(lines 79–88)
            Now, sir, young Fortinbras,
Of unimprovèd mettle hot and full,
Hath in the skirts of Norway here and there
Sharked up a list of lawless resolutes. . .
(lines 94–96)
But to recover of us, by strong hand
And terms compulsatory, those foresaid lands
So by his father lost. And this, I take it,
Is the main motive of our preparations,
The source of this our watch, and the chief head
Of this posthaste and rummage in the land.

Later in in the play’s first scene, Horatio provides the audience with useful background information about a past conflict between Denmark and Norway in which Prince Hamlet’s father defeated and killed the Norwegian king, Fortinbras. The details of this are further explained in Quotes by Setting: Elsinore, Denmark (the second quote).

Horatio’s explanation of the earlier conflict between King Hamlet and King Fortinbras sets up the first of many parallels between the two men’s sons, Prince Hamlet and Prince Fortinbras respectively. For one, both now live (uncomfortably) under the rule of uncles who assumed the throne upon their fathers’ deaths. The strongest link between them is that for each the death of his father was the defining moment of his life and he now lives to avenge that death.