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Preamble: A polemical introduction to the stable category.- The equivariant stable category.- Change of universe, smash products, and change of groups.- Equivariant duality theory.- Equivariant transfer.- The Burnside ring and splittings in equivariant homology theory.- Twisted half smash products and extended powers.- Operad ring spectra.- The homological analysis of extended powers.- Thom spectra.- Equivariant Thom spectra.