J. Peter May, The University of Chicago, IllinoisMona Merling, University of Pennsylvania, Philadelphia, PennsylvaniaAngelica M. Osorno, Reed College, Portland, Oregon.

• Introduction1. Preliminaries2. The simplicial and conceptual versions of the Segal machine3. The homotopical version of the Segal machine4. The generalized Segal machine5. The generalized operadic machine6. The equivalence between the Segal and operadic machines7. Proofs of technical results about the operadic machine8. Proofs of technical results about the Segal machine9. General topological groups and compact Lie groups10. Epilogue: Model categorical interpretationsA. Bearding functors $\mathscr {D}\longrightarrow G\mathscr {U}_*$B. Realization of levelwise $G$-cofibrations and $G$-equivalences