This is an advanced course on Computational Fluid Dynamics (CFD). Multidimensional hyperbolic conservation laws with emphasis on the Colella unsplit method for Euler equations. Higher order shock capturing schemes such as WENO. High-order compact finite difference schemes will be covered, and differences between high-resolution and high-order accuracy, dissipation vs. dispersion. Hybrid method such as the hybrid WENO-compact scheme. Pseudo-spectrum for stabiltiy analysis. Projection methods to solve the incompressible Navier-Stokes equations. Multigrid theory for the pressure Poisson equation. Advanced topics such as adaptive mesh refinement, fully implicit Newton-Krylov methods, preconditioning and parallel computing on modern supercomputing platforms.