A Short Introduction to Spectral Sequence

Spectral sequences were introduced by Leray in the 1940s and since then have become ubiquitous in algebra, geometry, topology. In this talk I will define what a spectral sequence is and how one can associate a spectral sequence to a filtered complex. Then I will explain how to construct the spectral sequence arising from a double complex (which is probably the most common way in which spectral sequences appear), and what kind of information one can hope to obtain about the cohomology of the complex from the spectral sequence. Along the way, I plan to include some examples from ring theory and group cohomology.