Homological Algebra is a branch of mathematics that studies algebraic structures using tools from topology and abstract algebra. It focuses on concepts like chains, complexes, and functors to analyze and classify mathematical objects, particularly in the context of modules and categories. One of the key ideas in Homological Algebra is the notion of exact sequences, which helps to understand how different algebraic structures relate to each other. This field has applications in various areas, including algebraic geometry, representation theory, and topology, making it a vital part of modern mathematics.