 The Serre Spectral Sequence by Allen Hatcher

By Allen Hatcher. Author-hosted Chapter1 draft of the spectral-sequence notes: pi.math.cornell.edu/~hatcher/SSAT/SSch1.pdf

Theorem1.3 gives the homology sequence and fundamental-group action; Theorem1.14, printed page24, gives cohomology, differential bidegrees and convergence to successive filtration quotients.