In this chapter, we analyze the case when the Lagrangian is invariant with respect to some one-parameter transformation, also known as symmetry. The symmetry may be coming from the physical symmetry of space-time, such as the symmetry with respect to rotations and translations in space or shifts in time. Alternatively, the symmetry may be less obvious. In any case, if that symmetry exists, we derive the powerful result known as Noether’s theorem, yielding a conserved quantity for that Lagrangian system. Conservations of angular and linear momenta and energy are written as Noether’s integrals coming from the symmetries of rotations and translations of space and time shifts, respectively.