I just bought Book of Unwritten Tales and in the list of files there is an update patch 1.01. I have found the 1.03 patch while searching the internet. Which one do i have to install?

From the King art games website:

We released the Patch 1.03 for the BOXED VERSION of The Book of Unwritten Tales yesterday.

ATTENTION: This patch is only relevant for the BOXED VERSION of the game, sold by Lace Mamba Global in some territories. If you own the digital download edition you don't need the patch, since this version has already been patched.

So it seems you don't need the 1.03 patch.