A chain complex is a mathematical structure used in algebraic topology and homological algebra. It consists of a sequence of abelian groups or modules connected by homomorphisms, where the composition of two consecutive homomorphisms is zero. This property allows for the study of algebraic invariants, which can reveal important information about topological spaces. In a chain complex, the groups are typically denoted as C_n, and the homomorphisms as d_n: C_n → C_{n-1}. The sequence is often visualized as a diagram, where each group represents a dimension, and the homomorphisms represent relationships between these dimensions. Chain complexes are fundamental in defining concepts like homology and cohomology.