Abstract: In this talk, I will give a brief overview of the orbital stability of standing waves in the nonlinear Schrödinger (NLS) equation, following the paper “Standing Waves in Nonlinear Schrödinger Equations” by Stefan Le Coz. I will first discuss the basic ideas of the NLS and solitary wave solutions, and then explain the Grillakis–Shatah–Strauss (GSS) method, which provides a rigorous framework for orbital stability based on the properties of the linearized operator and a slope condition.