I am taking Abstract Algebra now and it seems most of its examples come from elsewhere. For example, I know what permutations are in counting, but the kind Algebra studies seem to be somewhat different. And to me these concepts Algebra comes bundled with is the most difficult part of studying it. It's like studying Calculus without knowing anything in elementary algebra. Doable, but difficult.
What are some books I could study to close the gaps?
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Try this book. It seems like a good book to bridge the gap and it's free. http://abstract.ups.edu/ Also have you looked on the site, there are a quite few abstract algebra book recommendations. There may be book suggestions which meet your needs.
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If you're studying abstract algebra starting with group theory, Nathan Carter's Visual Group Theory is a great way to get used to the concepts before diving in deeper. On the other hand, if what you're having trouble with is proofs, sets, functions and relations, it could be worth picking up Daniel Velleman's How to Prove It or a similar book. Another idea, in preparation for studying rings and fields, is to study some elementary number theory first. In fact, some abstract algebra books begin that way, such as Lindsay Childs's A Concrete Introduction to Higher Algebra.
There might be, but a huge chunk of abstract algebra IS those examples. Learning about permutations (which are exactly what you know) with this language IS abstract algebra. A huge part of abstract algebra is knowing many different examples, things that you might not see elsewhere.
Although for a gentle introduction, Pinter is nice.