The invariant theory of finite groups is an important subject, of interest as a special case of more general invariant theory, for applications to other areas of mathematics, and in and of itself. In this talk, I will give Noether's proof of the finite generation of the ring of invariants of a finite group action, a proof which includes giving explicitly the generators, as well as Molien's Theorem on the number of linearly independent invariants of a given degree. References: Cox, Little, O'Shea "Ideals, Varieties and Algorithms 3e", Springer 2007 Stanley, Richard P. "Invariants of Finite GRoups and their Applications to Combinatorics" Bulletin of the American Mathematical Society Volume 1, Number 3, May 1979 http://www-math.mit.edu/~rstan/pubs/pubfiles/38.pdf Selig, J.M. "Notes on Molien's Theorem" http://myweb.lsbu.ac.uk/~ruthercg/MathsStudyGroup/SlidesAndNotes/Molien.pdf