Naive Set Theory
by Paul R. Halmos · Dover Publications
Paul Halmos's short classic on informal axiomatic set theory. Chapters 17–21 cover well ordering, transfinite recursion, ordinal numbers, sets of ordinals, and ordinal arithmetic in a few pages each, before moving to cardinals.
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More resources on Ordinals
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
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Reference article from the nLab research wiki giving the definition of ordinal numbers as well-ordered sets, their arithmetic, and constructive and structural variants. Suited to readers who know basic set theory and want precise statements, alternative formulations, and literature references.
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Unique free resource for going beyond textbook ordinal arithmetic into ordinal notations (epsilon-nought, Veblen functions) relevant to proof theory. First of John Baez's three-part Azimuth blog series on countable ordinals. Covers omega, ordinal addition, multiplication and exponentiation, Cantor normal form and epsilon-nought; Parts 2–3 continue through the Veblen hierarchy to the Feferman–Schütte and Veblen ordinals.
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Stanford course by Keith Devlin on how mathematicians reason, starting with the logic of language (and, or, not, implication, quantifiers) and moving to the structure of proofs, including contradiction and induction. Learners become able to read, construct and critique simple mathematical proofs.