ABSTRACT
This chapter introduces the most basic facts about the Lagrangian formalism. It formulates classical mechanics by starting from Hamilton's global variational principle, which employs the action of the system. This approach leads to the Euler-Lagrange equations of motion and their specific invariances. The Lagrange formulation of mechanics is particularly well-suited for treating questions concerning symmetries and conservation. The concepts of the Lagrangian formalism and the Noether theorem can be nicely extended to relativistic mechanics and to the framework of classical field theory. Noether's theorem provides the framework in which people can relate conserved quantities, the so-called constants of motion, to corresponding symmetries of the theory. The last specific Galilei symmetry people are going to consider is the one relating two reference frames moving with constant velocity to each other, the so-called Galilei boost symmetry.
