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 help in defining important concepts like homology and cohomology, which provide insights into the topological properties of spaces. They are essential tools for understanding how different algebraic structures relate to each other and for solving problems in various areas of mathematics.