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

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.

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 theorem stating that any spectral sequence converging to a graded module $H_*$ such that $E_{r}^{**}$ is bounded for all $r$, collapses at a finite stage.

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.

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