Abstract: 

We will start with a naive introduction to the symmetries of differential equations. After that, we will collect some ingredients necessary to understand Noether's first theorem, in which she proved that, for Euler-Lagrange equations, to each Noether symmetry associated with a Lagrangian, there corresponds a conservation law which can be determined explicitly through a formula. I will explain the working rule of Noether's first theorem through an illustrative example. Further, we will also discuss the Partial Noether approach for the construction of conservation laws.