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A sequence of interrelated chain complexes that allows the computation of algebraic invariants in homological algebra and algebraic topology.

The second page in the spectral sequence which often involves easier to compute homological invariants that will be refined in later pages.

The map $d_r: E_r^{p,q} \to E_r^{p+r,q-r+1}$ which connects different terms in the $r$-th page of a spectral sequence.

The process where the terms in the spectral sequence stabilize to the limit terms, often corresponding to the homology or cohomology groups of interest.

A specific type of spectral sequence used in the calculation of the homology and cohomology of fiber bundles.

A diagram of three modules and three module homomorphisms that give rise to a spectral sequence; the spectral sequence can be viewed as an iterative extraction of exact couples.

A nested sequence of subobjects ... $F^pA \subseteq F^{p+1}A \subseteq ... \subseteq A$ that is used to organize the construction of a spectral sequence.