This book arose out of the Workshop on structured ring spectra and their applications held in Glasgow in January 2002. Although it is not intended to be a proceedings of this conference, nevertheless the articles reflect the subject matter of the conference and the papers of Elmendorf, Robinson and Schwede have their origins in series of overview talks which these authors gave in Glasgow. All the papers published here have been refereed.

We would like to thank the London Mathematical Society, Edinburgh Mathematical Society and Glasgow Mathematical Journal Trust Fund for their financial support for the Workshop.

Since the middle of the 1990's there has been a renewed interest in structured ring spectra and several new models for the homotopy category of spectra of Boardman or Adams have been constructed, for example the category of S-modules constructed by Elmendorf, Kriz, Mandell and May [8], the category of symmetric spectra of Hovey, Shipley and Smith [11], the category of Γ-spaces constructed by Lydakis [13], the category of orthogonal spectra defined in [15] and [16], and many more. All of these categories possess a smash product which is strictly associative, commutative and unital, and therefore it makes sense to talk about monoids and commutative monoids, i.e., associative and commutative ring spectra.

Before these constructions have been found, one merely had a smash product of spectra which fulfilled associativity, commutativity only up to homotopy and therefore multiplicative structures on spectra were always given up to homotopy as well.