In this lecture, I will present two methods widely applied to show the orbital stability for special solutions of several Hailitonian PDEs.  One, due to Cazenave-Lions, is based on so-called concentration compactness priciple and the uniqueness of special soliutions. On the other hands, the other one, due to Weinstein and Grillakis-Shatah-Strauss, is based on the expansion of Hamiltonian and the nondegeneracy of special solutions. I aim to deliver these methods for NLS case and give an understanding that they are essentially the same. If the time permits, the Euler-Poisson case also can be death with.