Summary This paper summarizes and explains the concepts and methods of Stam's paper on Stable Fluids from a high-level perspective. Morris gives an overview of the Navier-Stokes equations, how these equations represent the problem of fluid simulation, and gives a brief background of the discretizations used prior to Stam's work. The paper then provides an overview of Stam's approach to solving the NS-equations, what contributions he made, and provides some details about his actual implementation. Stam's work is significant because he provides the first solution to the Navier-Stokes equations that is unconditionally stable for any timestep. Key Ideas 1. Stam uses Helmholtz-Hodge decomposition to make the vector field divergence-free. 2. Stam's biggest contribution is an unconditionally-stable, semi-implicit advection scheme.