But, good my brother,
Do not, as some ungracious pastors do,
Show me the steep and thorny way to Heaven
Whiles, like a puffed and reckless libertine,
Himself the primrose path of dalliance treads
And recks not his own rede.

Act 1, Scene 3 introduces us to Ophelia and Laertes and gives us a sense of what appears to be their strong sister-brother bond. In essence, Laertes does what brothers traditionally do when he warns his sister to be careful around Hamlet, and Ophelia responds by saying thanks for the advice on my love life. Then, with these lines she tells Laertes that he will do well to follow his own advice about being careful with romance when he gets to Paris. Read more about this quote in Quotes by Character: Ophelia (the first quote).

Give thy thoughts no tongue,
Nor any unproportion’d thought his act.
Be thou familiar, but by no means vulgar.
Those friends thou hast, and their adoption tried,
Grapple them unto thy soul with hoops of steel;
But do not dull thy palm with entertainment
Of each new-hatch’d, unfledg’d comrade. Beware
Of entrance to a quarrel; but, being in,
Bear’t that the opposed may beware of thee.
Give every man thine ear, but few thy voice:
Take each man’s censure, but reserve thy judgment.
Costly thy habit as thy purse can buy,
But not express’d in fancy; rich, not gaudy:
For the apparel oft proclaims the man;
And they in France of the best rank and station
Are most select and generous chief in that.
Neither a borrower nor a lender be:
For loan oft loses both itself and friend;
And borrowing dulls the edge of husbandry.
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.
 

Polonius’s advice to his son Laertes in this passage from Act 1, Scene 3 is one of the most famous and most discussed speeches in Shakespeare’s plays—largely because of it poses the question of whether advice can be useful even when the character and motivations of the person delivering it are suspect. This full speech is discussed at length in Famous Quotes Explained. The most famous line from Polonius’s speech (“This above all,—to thine own self be true”) is the subject of a separate discussion below.

This above all,—to thine own self be true
 

This is the most quoted line from Polonius’s famous speech offering fatherly advice to his son Laertes just prior to Laertes’s departure for Paris for schooling. This line and the ones immediately after it (“And it must follow, as the night the day, / Thou canst not then be false to any man.”) are the culmination of Polonius’s speech, and the sentiment that he is expressing is that being honest with yourself is crucial because it means you will be honest with everyone else.

While this sensible advice in and of itself, there is a problem with these words and the overall soliloquy because Polonius’s many dubious character traits might be seen as disqualifying him from being reliable source for life coaching. While we have no reason to doubt Polonius’s love for his son, taking his flaws into account tinges his words so that they can sound more like mere platitudes than sage advice from a wise father.

In few, Ophelia,
Do not believe his vows

Here, Act 1, Scene 3 ends as it began—with a close family member advising Ophelia not to trust Hamlet’s profession of love. Earlier this advice came from her brother, Laertes, and her it comes from her father, Polonius. The reasons for Polonius and Laertes warning her and consequences of Ophelia accepting their advice are discussed in Quotes by Character: Ophelia (the second quote).