Starting from Newton’s laws, we define the concept of the Lagrangian and derive the celebrated Euler-Lagrange equations that will form the foundation of this book. Using Euler-Lagrange equations, we also derive the concept of energy, which is, in general, not equal to kinetic plus potential energy. We show that the energy is conserved whenever the Lagrangian is independent of time. We then use these newly derived Euler-Lagrange equations to compute the celebrated laws of planetary motion derived empirically by J. Kepler and explained by Newton.