The book Hamlet is reading is vital for understanding the play.
(Copied from Remembrances in the Book of Their Brains
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http://www.thyorisons.com/index.html#Remembrances )
The book full of old men is very important.
It is the book Polonius sees Hamlet reading.
It is also the book that Polonius later gives to Ophelia to occupy her mind.
It is also the book of remembrances that Hamlet doesn't remember when Ophelia tries to return it to him.
It is the book of orisons wherein Hamlet wants Ophelia to remember all his sins.
It is the book of Hamlet's brain from which he erased himself and wrote his father's commandment. It is also the book of Ophelia's brain, where she let her father tell her what to think and let her brother keep the key to her memory.
It is a document in madness. It is a book full of old men - it should be dusty.
LORD POLONIUS (to Ophelia)
. . . .
Read on this book;
That show of such an exercise may colour
Your loneliness. . . . .
OPHELIA
My lord, I have remembrances of yours,
That I have longed long to re-deliver;
I pray you, now receive them.
HAMLET
No, not I;
I never gave you aught.
OPHELIA
My honour'd lord, you know right well you did;
And, with them, words of so sweet breath composed
As made the things more rich: their perfume lost,
Take these again; for to the noble mind
Rich gifts wax poor when givers prove unkind.
There, my lord.
Since he IS a student, maybe Hamlet could take a shiny new book out of his backpack when he writes his father's commandment in the book and volume of his brain. Then when he writes his uncle in his tables, he could take out the book again (now dusty) and write his uncle in the back of the book, as an appendix.
At the end of the scene where Hamlet is reading the dusty book, Polonius could leave with the book in hand (Hamlet having willingly parted with the book of his brain) so that Polonius can later hand the book to Ophelia.
LORD POLONIUS
. . .--My honourable lord, I will most humbly take my leave of you.
HAMLET
You cannot, sir, take from me any thing that I will more willingly part withal: except my life, except my life, except my life.
Also please see Old Men in the Book of his Brain
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http://www.thyorisons.com/index.html#Old_Men
and
A Document in Madness
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http://www.thyorisons.com/index.html#Document_Madness