Most of us have learned the basics of Newtonian mechanics. Newtonian mechanics is also called vectorial mechanics because it studies the motion of bodies under the influence of vector quantities such as force. However, Newtonian mechanics is not convenient in solving certain problems. There are other frameworks in theoretical physics called analytical mechanics such as Lagrangian mechanics and Hamiltonian mechanics. They are equivalent to Newtonian mechanics and they use scalar quantities such as the kinetic energy and potential energy of a system to derive the equations of motion of the system. In many problems, they appear to be more elegant and succinct than Newtonian mechanics. More importantly, the concepts in analytical mechanics can be generalized to hyperspace/phase space, in which we do not live. Moreover, Hamiltonian mechanics allow us to transition from classical mechanics to quantum mechanics more “smoothly.” In this chapter, we will learn the skills of using Lagrangian and Hamiltonian mechanics. Readers are expected to learn the rules only.