I have iPad and iPod touch. Both I bought just for reading books in pdf format.
If it is possible, I want to create some folders to separate the books based on categories I will define.
Yes, as long as you're running the latest version.
Poof, they're now out of the default "Books" collection and now in the collection you chose.
Yes, with the latest iBooks it is possible to create your own categories of books. When in your iBooks library on the iPod, tap the middle button at the top, it will probable read Books or PDFs, to create/edit your categories. The same functionality is found by tapping the Categories button on the iPad iBooks.
Once you have the categories you want, you can move books into them by tapping the Edit button in the library view, tapping the books to select them and then tap the Move button. Select the category you want, and press done.
You can then switch between categories from the same screen that you created them.