Abstract: Emmy Noether, German female mathematician, published in 1918 an important paper, entitled "On Invariant Functionals", in which two theorems are proved. The first theorem is about the symmetries and the invariants in classical mechanics; the second theorem is about the general relativity. Noether's first theorem is now a basis not only for classical mechanics and classical field theory, but also for the studies of symmetries and invariants in quantum mechanics and quantum field theory. This paper gives an introduction to her paper and the development her ideas, as well as the Noether's theorem in classical mechanics.