I have written up some detailed lecture notes
Introduction to Stable homotopy theory
Prelude -- Classical homotopy theory (pdf, 99 pages)
Part 1 -- Stable homotopy theory
Part 1.1 -- Sequential spectra (pdf, 67 pages)
Part 1.2 -- Structured spectra (pdf, 80 pages)
Part 2 -- Adams spectral sequences (pdf, 56 pages)
This introduces and then proceeds systematically via model categories. Full details and proofs are given.
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