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Introduction 1 1. Spectra and the stable homotopy category 6 2. Smash products and twisted half-smash products 11 3. The category of L-spectra 13 4. The smash product of L-spectra and function L-spectra 15 5. The category of S-modules 19 6. S-algebras and their categories of modules 21 7. The smash product of R-modules and function R-modules 24 8. Tor and Ext in topology and algebra 28 9. Universal coefficient and Künneth spectral sequences 31 10. Algebraic constructions in the derived category of R-modules 33 11. R-ring structures on localizations and on quotients by ideals 36 12. The specialization to MU-modules and MU-ring spectra 38 References 40