Polonius

Polonius:
"At such a time I'll loose my daughter to him
[to the King] Be you and I behind an arras then.
Mark the encounter. If he love her not,
And be not from reason fall'n thereon,
Let me be no assistant for a state,
But keep a farm and carters." (2.2.176-181)

Polonius has gone to the king, claiming Hamlet has gone mad because he is so deeply in love with Ophelia. The King and Queen call on Hamlet's old friends, Rosencrantz and Guildenstern to spy on Hamlet to find out why he is not himself. The term "loose" is in the side-note as releasing an animal from its chains, either for hunt or for purposes of mating. Polonius is putting his daughter out in a scheme to get on the King's good side. He is going to send her out to Hamlet, and if it is seen that Hamlet is not in love with her, everyone will know that his madness is not because Polonius has forbidden Ophelia to see him. 

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Polonius:
"Your bait of falsehood take this carp of truth;
And thus do we of wisdom and of reach,
With windlasses and with assays of bias,
By indirections find indirections out." (2.1.70-73)

This is another passage where Polonius is scheming to get the truth out. This time it is not his daughter, but his son, Laertes. He has called on a man named Reynaldo to spy on Laertes while spreading rumors and lies about him. What he is saying to Reynaldo is a metaphor explaining that telling lies is how he is going to find the truth about what Laertes is up to in Paris. This is an example of how Polonius is willing to sabotage his son's reputation, which is hypocritical because Polonius is all about how one should present themselves.
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Polonius:

Give thy thoughts no tongue,

Nor any unproportioned 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-hatched, unfledged comrade. Beware

Of entrance to a quarrel, but being in,

Bear ’t that th' opposèd may beware of thee.

Give every man thy ear but few thy voice.

Take each man’s censure but reserve thy judgment.

Costly thy habit as thy purse can buy,

But not expressed in fancy—rich, not gaudy,

For the apparel oft proclaims the man,

And they in France of the best rank and station

Are of a 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,

This is Polonius's pep talk to Laertes about how to please everyone and how he should present himself in Paris, because Polonius does not want his son to make a fool of his family. The speech ends up being very ironic considering the first line of the passage is advice to Laertes to not say what he's, when the last line is to, above all, "just be yourself". His fatherly advice before his son leaves for Paris is basically to be seen and not heard. Polonius is treating his son like a child. He even feels to need to remind his son that apparel is the way to announce one's status publicly, and therefore must dress wealthily but not gaudy. 

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Polonius:

"Ophelia, 

Do not believe his vows, for they are brokers,

Not of that dye which their investments show" (1.3.136)

Although Polonius does not have many sides to his character, he has different faces he puts on, each for his children, Reynaldo, and even the King. His character is not very paternal; He uses his children attempting to raise his status. Polonius is talking with his daughter about her relationship with Hamlet. As a father, Polonius should be concerned about his daughter's relationship to watch out for her, however in this line Polonius is referencing business. As we later see, Polonius does not even care about his daughter's feelings for Hamlet because to him, their relationship is like a business opportunity. He can use their relationship as a way to talk to the King.