In this talk we will discuss the spectral sequence of a filtered complex, which is one of the main computational techniques in homological algebra. The point of departure will be the degenerate case that is commonly referred to as the long exact sequence in cohomology.
This will be followed by a brief recapitulation on filtrations and some generalities on spectral
sequences. We will focus on examples and applications, such as the Atiyah-Hirzebruch spectral sequence, the Grothendieck spectral sequence, and the Hodge-to-de Rham spectral sequence.