A spectral sequence is a mathematical tool used in algebraic topology and homological algebra to compute complex algebraic structures. It organizes information into a sequence of pages, each containing a series of groups or modules that approximate the desired object. The process involves taking successive approximations, allowing mathematicians to analyze and simplify complicated problems. Spectral sequences arise in various contexts, such as the study of cohomology and homotopy groups. They can also be applied in sheaf theory and derived categories, providing a systematic way to handle computations that would otherwise be intractable.