Again, an allusion is an indirect reference to a work of literature. A very common allusion to Shakespeare's Hamlet is found in the common truism: "This above all: to thine own self be true." Ironically, this little bit of wisdom is actually spoken by Polonius, the fool of the play. Nonetheless, these words have something important to impart. These words are a departure from the silly explanation of proper etiquette given in the first half of Polonius's long speech. Just as in the first common allusion from Polonius, this second one can be seen with greater clarity if the full three lines are read:
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 (Act I, Scene 3, lines 77-79).
Put simply, if you are true to yourself and who you really are, just as the sun always rises each morning, then there is no way you will be a liar to anyone you meet. You will always project truth because it will emanate from your very being.
A bit of irony here is that immediately after Polonius instructs his son to be true to himself, he instructs his daughter otherwise. Ophelia spends her first words of this play trying to show her dad how Hamlet is quite an honorable potential husband by saying that "he hath, my lord, of late made many tenders / Of his affection to me. . . He hath importuned me with love / In honorable fashion." Polonius immediately causes Ophelia to doubt herself, "Do you believe his tenders, as you call them?" Ophelia reneges and promises to "obey" her dad in not receiving Hamlet's advances. So much for being true to oneself. According to Polonius, I suppose that should only apply to sons and not to daughters or when what the parent.
Just to end on a humorous note here. The reason why even this piece of wisdom can seem to cement Polonius as the fool of the play is because, just as Polonius is instructing his own son to be true to himself, Polonius rarely has clarity about anything at all. In fact, most often he can be seen vacillating between one thought and another or, in his most famous death scene, actually hiding in order to gain more information. For someone doling out the wisdom of "to thine own self be true," Polonius certainly spends all the rest of his time questioning and doubting everyone else. Polonius cannot take his own simple, yet important, advice.