to give up something = to stop doing something, to refrain from (doing) something, e.g. to give up smoking/(eating) chocolate
to give up on something/someone means to abandon something/or someone, usually after several attempts with no success, e.g. to give up on writing a novel.
So, they are similar, but different. You'd never say give up on smoking, for example. However, in some cases, the meanings are so similar that they're actually interchangeable.
I don't want to give up learning = I don't want to stop learning.
I don't want to give up on learning = I don't want to abandon learning.
As you can see, very similar. I'd say the latter version, with on, implies that the person has been trying to learn, but continually failing, but nonetheless does not want to give up; whereas the former version implies that the person has been successfully learning and does not want to stop.
Context: Suppose some native speakers just told me that the book I had been reading was poorly written and riddled with spelling and grammatical errors. I hadn't realized the problems until they told me, so I decided to give up on that book based on their criticism.
In this case, should I use "I gave up the book when they told me the book was poorly written"? I stopped reading it in no time after the native speakers said it was a poor book.
Is "I gave up on the book" more appropriate in a context where I couldn't bear to finish a book after several attempts with no success?
I would "give up on" the book, not "give up the book".
To say "I gave up the book" seems to me to say that I donated the book to someone else
"I gave up on the book," is a common, natural way to say that I stopped reading it for some reason.
Thanks panjandrum~~ I agree with you on all counts. It seems like there's no hard and fast rule as to the difference between them, and I have to learn their use on a case-by case-basis. As for your explanation of "I give up the book", instead of donating the book, how about throwing it in the bin?
Suppose I've been having a restless night and struggling to fall asleep for hours. I've tried various methods from counting sheep to narcotic sleep pills, but still, my eyelids have refused to get heavy. If I stop trying to get myself to sleep and go out for a walk, would it make sense to use "give up on" in "I've decided to give up on sleeping"?