Invariant theory is the root of modern algebra. The general problem of classical invariant theory is to describe the invariant ring of polynomial ring under the action of some certain groups. In this talk I will introduce Hilbert's proof of the finite generation property of invariants. I will not go to the most general case but want to give the concepts. Hopefully I can talk about the geometric interpretation of Hilbert's Fourteenth Problem due to Zariski and a brief description of geometric invariant theory. The background knowledge is basic commutative algebra, such as Hilbert basis theorem. It will be appreciate if you know the definitionof algebraic varieties and Lie algebra. The references are 1. Igor Dolgachev, Lectures on Invariant Theory, Cambridge University Press, 2003. 2. David Eisenbud, Commutative Algebra, Springer-Verlag, GTM 150