This chapter is concerned with differential equations admitting a variational formulation. Starting from a Lagrangian function, and using Hamilton principle (or principle of least action), the procedure for deriving Euler–Lagrange equations is described. Then, the invariance of the Lagrangian action functional under a Lie group of transformations is analyzed. So, Noether theorem for constructing conservation laws is proved. In the context of classical mechanics, Noether theorem yields first integrals; on the contrary, in Lagrangian field theory, where we may have general Lagrangian functions of order \(r\ge 1\) in n independent variables, Noether theorem gives conservation laws. Some meaningful examples where Noether theorem yields conservation laws are discussed.