Every several years I borrow my colleague George's copy of The Joy of Sets by Keith Devlin and attempt to learn some set theory. The first time, ca. 1993, I crashed and burned on page 16 (section 1.7, "Well-Ordering and Ordinals"). On my second attempt to climb the mountain, ~2002, I reached page 29 and then fell into an infinite crevasse ("The Zermelo-Fraenkel Axioms"). This month I changed tactics and jumped on the magical mystery bus carrying only a tourist visa. I skipped by the proofs, slid past the exercises, skimmed the hard parts, and made it to the end of the line having glimpsed some of the deep inner workings of the universe.
Set theory is so fundamentally fascinating because it's so damnably fundamental. It's the machine language of mathematics. Like subatomic physics, sets come as close to bedrock as you can dig. But as Devlin himself says in the Preface, "... although set theory has to be developed as an axiomatic theory, occupying as it does a well-established foundational position in mathematics, the axioms themselves must be 'natural'; otherwise everything would reduce to a meaningless game with prescribed rules."
I admit: there were times that I thought I was witnessing a meaningless game of symbol-shuffling. But eventually Devlin somehow explained the sense in the situation, or at least convinced me that sanity was within reach. I still don't understand (most of) modern set theory, but this morning I respect it. The Joy of Sets has given me a glimpse of the major constellations, a map of where the stars live. That's all my brain can handle. Maybe I'll take a running start and try again in 2018.
(a significant glitch that I noted in the book, explained in the online errata: a key symbol for "function restriction" was not printed in 70 instances, on 21 pages, Oops! And cf. No Concepts At All (2001-02-22), LogicAndInformation (2001-08-01), MillenniumMath (2002-12-05), ThirdNormalForm (2004-02-28), GatewaysToMathematics (2004-05-20), StayingTheCourse (2005-07-11), ...) - ^z - 2010-06-25