The book contains a detailed and comprehensive historical introduction describing the development of operad theory from the initial period when it was a rather specialized tool in homotopy theory to the present when operads have a wide range of applications in algebra, topology, and mathematical physics. Many results and applications currently scattered in the literature are brought together here along with new results and insights. The basic definitions and constructions are carefully explained and include many details not found in any of the standard literature.
There is a chapter on topology, reviewing classical results with the emphasis on the $W$-construction and homotopy invariance. Another chapter describes the (co)homology of operad algebras, minimal models, and homotopy algebras. A chapter on geometry focuses on the configuration spaces and their compactifications. A final chapter deals with cyclic and modular operads and applications to graph complexes and moduli spaces of surfaces of arbitrary genus.
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