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It's been quite some time since I took a foundational course in proof writing in mathematics, which covered elementary topics in the carnality of sets. I'm looking to brush up on that unit, and I'm looking for a resource to help me do so. The last thing I want is to go back to a foundations textbook and start reading scores of chapters in this topic. Rather, I'm looking for a(n) (online resource), preferable a chapter or a set of notes, that cover the basics: from the definitions of finite/infinite sets to the basics of Axiom of Choice etc., the necessary material required to go through almost all undergraduate level texts in mathematics, without rigorously going in the details of advanced set theory.

Any recommendations?

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Halmos's Naive Set Theory might be good for you. It was intended for undegraduate math students and it presents the concepts without getting into too much advanced things.

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    I'll look into it. I just want a set notes/chapters which I can read quickly to freshen up my memory (which is size of a peanut, honestly) on the basics results, so as to quickly review them whenever I see them being used somewhere else. – 2017-01-09