This work is an attempt to explain in some detail section III D of the paper: N.J.A. Sloane. "Error-correcting codes and Invariant Theory: New application of a Nineteenth-Century Technique". For that, we will be concerned with polynomial invariants of  finite groups which come from a group action. We will introduce the basic notions of Invariant Theory to give an almost self-contained proof of Molien's theorem, and also present applications on linear codes.