Lagrange's Equations are a set of mathematical formulas used in classical mechanics to describe the motion of a system. They are derived from the principle of least action, which states that the path taken by a system is the one that minimizes the action, a quantity that combines kinetic and potential energy. These equations are particularly useful for analyzing complex systems with multiple degrees of freedom. In Lagrange's framework, the motion of a system is expressed in terms of generalized coordinates, which simplify the equations of motion. This approach allows for easier handling of constraints and non-conservative forces, making it a powerful tool in fields like physics and engineering.