Lyapunov's Theorem is a fundamental result in the field of stability theory, particularly in the study of dynamical systems. It provides criteria to determine the stability of equilibrium points in nonlinear systems. By constructing a Lyapunov function, which is a scalar function that decreases over time, one can show that the system will remain close to the equilibrium point. The theorem is named after the Russian mathematician Alexandr Lyapunov, who developed these concepts in the late 19th century. Lyapunov's work has significant applications in control theory, robotics, and various engineering fields, helping to ensure that systems behave predictably and remain stable under perturbations.