Speaking as a PhD in pure math: It's a great book, but I would not recommend it at all for someone trying to get the gist of the theorem. GEB is a book for thos

Speaking as a PhD in pure math: It's a great book, but I would not recommend it at all for someone trying to get the gist of the theorem. GEB is a book for those who already have a strong self-interest in or prediliction to the intricacies of mathematical logic. It's a long book and is likely to be off-putting for those wanting a practical approach. Raymond Smullyan's book (another reply to the OP) is a much better choice.