What does the Book with Seven Seals contains? We know what happens when each of the seven seals are broken. But there's no more mention of this book once the seals are broken.   

What does this book contain?
Does the Lamb actually read it's content?
What happens to it afterwards, once the seals are broken?  

This is difficult to understand.
@Allen Fuller's answer is a good summary of what people think is contained in the Seven Seals. The key is in the wording: they are called seals. The meaning is sealed up, hidden.

Consider what the angel told Daniel:


  “The vision of the evenings and mornings that has been given you is
  true, but seal up the vision, for it concerns the distant future.”
  (Daniel 8:26)


One commentator (Ellis Skolfield) believes that Daniel rearranged the chapters of his book to make the pattern more complicated, to deter others from gaining full understanding until God so wills.

Consider what another angel told John:


  And when the seven thunders spoke, I was about to write; but I heard a
  voice from heaven say, “Seal up what the seven thunders have said and
  do not write it down.” (Revelation 10:4)


In this case, John was told to not even write it down.

I believe that the Seven Seals are just that - messages that are not for our eyes. Until it is all over, we won't be told what is in them. At best, their contents will be revealed very close to the end, to guide believers when times are darkest.