This concise monograph presents a rigorous treatment of systems of conservation laws with bounded variation and their stability properties. Drawing on techniques from the theory of partial differential equations, the author develops existence and uniqueness results for Cauchy problems, examines the structure of shock waves, and establishes stability estimates that are essential for both theoretical analysis and numerical approximation. The work integrates functional analytic methods with classical hyperbolic theory, offering a clear exposition that bridges abstract mathematics and applications in physics. Intended for researchers and advanced graduate students in analysis and mathematical physics, the text provides a solid foundation for further study of nonlinear wave phenomena and related conservation principles.