Spectral sequences are one of the most effective
computational tools in algebraic topology.
Spectral sequences are introduced by J. Leray.
Leray’s spectral sequence was translated into
the form suitable for algebraic topology by
J.P. Serre and served as a powerful tool in
the developement of the early stage of algebraic
topology. The reader is recommended to read
McCleary’s
[
McC99
]
.
The study of spectral sequences can be split into the
following two parts.

general theory of exact couples and spectral
sequences

constructions of spectral sequences motivated by
topological problems and computations of
(co)homology
