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The Burnside ring of finite G-sets.- The J-homomorphism and quadratic forms.- ?-rings.- Permutation representations.- The Burnside-ring of a compact Lie group.- Induction theory.- Equivariant homology and cohomology.- Equivariant homotopy theory.- Homotopy equivalent group representations.- Geometric modules over the Burnside ring.- Homotopy-equivalent stable G-vector bundles.