How we cite our quotes: (Act.Scene.Line) according to the Norton edition
Quote #1
QUEEN GERTRUDE
Why seems it so particular with thee?
HAMLET
'Seems,' madam? Nay it is. I know not 'seems.'
'Tis not alone my inky cloak, good mother,
Nor customary suits of solemn black,
Nor windy suspiration of forced breath,
No, nor the fruitful river in the eye,
Nor the dejected havior of the visage,
Together with all forms, moods, shapes of grief,
That can denote me truly. These indeed 'seem,'
For they are actions that a man might play:
But I have that within which passes show,
These but the trappings and the suits of woe.
(1.2.78-89)
From his very first scene, Hamlet sets himself up as someone who hates deception and values inner truth above all. Here, he insists that outward appearances (like his "inky" black clothing, sighs, and tears – all the common markers of grief) can't possibly "denote" what's truly inside him. In other words, Hamlet's saying that his anguish and grief over his father's death are far more intense than they appear to the outside world. He's also implying that Gertrude, Claudius, and the rest of the court are totally fake and disingenuous because they don't care about him or his feelings at all and are far too concerned with keeping up appearances.
Quote #2
POLONIUS
This above all: to thine own self be true,
And it must follow, as the night the day,
Thou canst not then be false to any man.
(1.3.84-86)
Polonius likes to dish advice, but he sure can't take it. Given Polonius' penchant for spying on his children and Hamlet in order to curry favor with King Claudius, he's not in any position to be talking about truth.
Quote #3
GHOST
Ay, that incestuous, that adulterate beast,
With witchcraft of his wit, with traitorous gifts—
O wicked wit and gifts, that have the power
So to seduce!—won to his shameful lust
The will of my most seeming-virtuous queen.
O Hamlet, what a falling-off was there!
From me, whose love was of that dignity
That it went hand in hand even with the vow
I made to her in marriage, and to decline
Upon a wretch whose natural gifts were poor
To those of mine.
But virtue, as it never will be moved,
Though lewdness court it in a shape of heaven,
So, lust, though to a radiant angel linked,
Will sate itself in a celestial bed,
And prey on garbage.
(1.5.49-64)
Like Hamlet, the ghost dwells on Gertrude's "seeming" virtue. But is the ghost saying Gertrude cheated on him when they were married? Or, does the ghost merely see her remarriage as a betrayal? We get stuck on the meaning of "adulterate," which, in Elizabethan England could refer to a cheating spouse or any sexual sin in general (like incest). Either way, the ghost implies that Gertrude's remarriage retroactively makes their marriage into a sham.