Topologists are fond of their machinery. As the title of this book indicates, my intention is to provide a user's manual for the class of complicated algebraic gadgets known as spectral sequences.

A ‘good’ user's manual for any apparatus should satisfy certain expectations. It should provide the beginner with sufficient details in exposition and examples to feel comfortable in starting to apply the new apparatus to his or her problems. The manual should also include enough details about the inner workings of the apparatus to allow a user to determine what is going on if it fails while in operation. Finally, a user's manual should include plenty of information for the expert who is looking for new ways to use the device. In writing this book, I have kept these goals in mind.

There are several classes of readers for whom this book is written. There is the student of algebraic topology who is interested in learning how to apply spectral sequences to questions in topology. This reader is expected to have seen a basic course in topology at the level of the texts by [Massey91] and [May99] on singular homology theory and including the definition of homotopy groups and their basic properties. This beginner also needs an acquaintance with the basic topics of the homological algebra of rings and modules, at the level of the first three chapters of the book of [Weibel94].

The next class of reader is principally interested in algebra and he or she wants an exposition of the basic notions about spectral sequences, hopefully without too much topology as prerequisite.