I particularly liked the section where Harry is trying to find out how magic "works". He starts with the gross physicalities: the materials the wands are made of, the sounds of the recited spells. He ends up with the mathematics underlying physics, learning how to create new spells. He uses his new found knowledge to create a very powerful weapon spell he uses to kill a mountain troll. If you want to know how the spell works, you'll have to read the book. I highly recommend it. (I've read it more than once.)