The Lagrangian Formulation is a method in classical mechanics that reformulates Newton's laws of motion. It uses the concept of the Lagrangian, which is defined as the difference between kinetic and potential energy. This approach allows for the analysis of complex systems and constraints by applying the principle of least action, which states that the path taken by a system is the one that minimizes the action. In this formulation, the equations of motion are derived from the Euler-Lagrange equations. These equations provide a systematic way to derive the dynamics of a system, making it easier to handle problems in mechanics, especially when dealing with multiple degrees of freedom or non-conservative forces.