You may take this book if you like.
You can take this book: it is not heavy.
You need not take this book.
I cannot take this book.
Just think: we need not have gone there!
You need not agree at once: think a few days.
You may go there today.
You need not go there today.
You need not rewrite the essay.
You can stay: you have time, don’t you?
You may stay if you like.
You need not stay if you don’t want to.
You need not tell him about it.
You may tell him about it.
We need not repeat these rules: we know them.
We need not have written the essay.
He need not have come: everything had already been done.