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, called boundary maps, which satisfy a specific condition: the composition of two consecutive maps is zero. This means that the image of one map is contained in the kernel of the next, allowing for the study of algebraic invariants. Chain complexes are essential for defining concepts like homology and cohomology, which help classify topological spaces. They provide a framework for analyzing the relationships between different algebraic structures and their geometric counterparts, facilitating deeper insights into their properties.