I have just bought my first house in Whiterun however there is no bookshelves. I have checked all the shops and I don't see where I can purchase any.

Does anybody know if this is possible?

Decorate your home (living room and alchemy room I think) with the steward and bookshelves will be added.

Sorry to ask but where is the steward?

He's the one you bought the house off in the first place. You can find him in Dragonreach (the main keep of Whiterun), usually with the Jarl.

The alchemy upgrade has a bookshelf.

Thanks guys!!!