I would like to know which books on mathematics (from university texts to divulgative pop-math books) inspired you the most.
My choice is Spivak's Calculus, which is, IMHO one of the most inspirational mathematics books I've ever read: it has very meaningful examples and clear explanations.
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Honestly, though it's not exactly a text for mathematicians, Quine's Methods of Logic basically kicked off my interest in mathematics. It's the text I taught myself formal logic from, and the text in which I started to appreciate the beauty of formal logic.
Probably second is Goldblatt's Topoi, which introduced me, in one fell swoop, to category theory, topos theory, a smattering of topological ideas, and most of my basic set theoretic concepts. Most of the math I learned subsequently was originally part of an effort to understand this book better.
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The Princeton companion to mathematics is surely a tour de force. It is a joint effort of many leading mathematicians, and show the beauty of mathematics rigorously in an inspiring way.
I'll second Spivak, but I was also inspired by E.T. Bell's Men of Mathematics, which has a lot of math content. And not a book per se (though there are collections), Martin Gardner's columns in Scientific American were also inspiring.