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A user’s guide to spectral sequences. 2nd ed. (English) Zbl 0959.55001
Cambridge Studies in Advanced Mathematics. 58. Cambridge: Cambridge University Press. xv, 561 p. (2001).
The first edition of this excellent book has been reviewed in Zbl 0577.55001.
The biggest change in the second edition is the addition of two chapters. The new chapter $$8^{\text{bis}}$$ treats non simply-connected spaces, more specificly: nilpotent spaces. The Cartan-Leray spectral sequence and Lyndon-Hochschild-Serre spectral sequences are discussed. The new chapter 10 treats Bockstein spectral sequences in more detail. For a survey of the other chapters refer to the review of the first edition.

##### MSC:
 55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology 55Txx Spectral sequences in algebraic topology 57T35 Applications of Eilenberg-Moore spectral sequences 18G40 Spectral sequences, hypercohomology 57T15 Homology and cohomology of homogeneous spaces of Lie groups 55R40 Homology of classifying spaces and characteristic classes in algebraic topology 55R20 Spectral sequences and homology of fiber spaces in algebraic topology 55Q40 Homotopy groups of spheres 55Q45 Stable homotopy of spheres 55M05 Duality in algebraic topology 57R19 Algebraic topology on manifolds and differential topology 55U10 Simplicial sets and complexes in algebraic topology 17B56 Cohomology of Lie (super)algebras 20J05 Homological methods in group theory 18F25 Algebraic $$K$$-theory and $$L$$-theory (category-theoretic aspects) 18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) 22E41 Continuous cohomology of Lie groups