The first edition of this book served as my introduction to the mysteries of spectral sequences. Since writing it, I have learned a little more in trying to do some algebraic topology using these tools. The sense that I had misrepresented some topics, misled the reader, even written down mistaken notions, grew over the years. When the first edition came to the end of its run, and was going out of print, I was encouraged by some generous souls to consider a second edition with the goal of eliminating many of the errors that had been found and bringing it somewhat up to date.

The most conspicuous change to the first edition is the addition of new chapters—Chapter 8bis on nontrivial fundamental groups and Chapter 10 on the Bockstein spectral sequence. In Chapter 8bis (an address, added on after Chapters 5 through 8, but certainly belonging in that neighborhood), I have found a natural place to discuss the Cartan-Leray and the Lyndon-Hochschild- Serre spectral sequences, as well as the important class of nilpotent spaces. This chapter is an odd mixture of topics, but I believe they hang together well and add details to earlier discussions that depended on the fundamental group. Chapter 10 acknowledges the fundamental role that the Bockstein spectral sequence plays in homotopy theory, especially in the study of H-spaces. It is as much a basic tool as the other spectral sequences of Part II.