Can I purchase an iBook as a gift for someone else?

If you select the down arrow next to the price of the book there is an option to gift it.

I saw your response, but I don't see a down arrow or any arrow next to the price of the book in iBooks?

If you're using an iOS device it's different:

http://support.apple.com/kb/HT2736?viewlocale=en_US&locale=en_US

If I am sending a book as a gift via iTunes, how does the person open it up in iBooks, if does it automatically open up in iBooks. I just don't want any difficulty for my father to open and enjoy his book. Would I be better to just download it directly onto his ipad and not have it as a gift for him, could there be some technical or other difficulties for him?

Your father can redeem it through the iBooks Store:

http://support.apple.com/kb/TS5352