Useful language for your introduction:
I am writing to you because...
I have read your book .......... and ..........
I have recently taken your book ............ out of our school library, .........
A friend at school has recently recommended your book ....... to me.
I saw that your book ....... has recently won a prize for literature and .....
I heard a review of your new book on the radio (televison/podcast ) so I rushed out to buy it.
After I had read the great review of your new book in the newspaper, I ..........