Equivariant stable homotopy theory / L. G. Lewis, Jr., J. P. May, M. Steinberger ; with contributions by J. E. McClure

... the book contains all the basic material on equivariant stable homotopy theory including as a particular merit, of course, the first construction of a satisfactory category of G-spectra. Its emphasis is on the categorical viewpoint, using the appropriate language and theory of adjoint functors for many of the useful constructions in equivariant homotopy theory. It will almost certainly become the basic standard reference in the field.

Whereas the book’s intention is the foundation of equivariant stable homotopy, it seems not to adress itself to the novice, but rather to the expert reader. This impression is supported by the style of writing, at least in respect to the organization of the presented material. Of course it could be argued that questions of style should be regarded as a matter of taste. Nevertheless the reviewer holds that especially in the more foundational chapters I, II, VI, VII the exposition could have been much more systematic. Many forward references, delays of important proofs, explanations in terms of notions which are developed later or elsewhere, references to unpublished sources make for hard reading if one has not yet obtained an overview over the whole contents. But still, for the reasons indicated above, it is certainly worth the trouble to work one’s way through this book. (Zentralblatt)