Computational Fluid Dynamics I is a first course to introduce the modells and numerical methods for simulating fluid dynamics. Fluid dynamics problems are given in all flow and transport problems, e.g., fluid flow or gaseous flow. The main equation is the Navier-Stokes equation. We derive the fluid dynamical equation based on the Euler equations from the microscopic model. Then we present the main numerical methods, e.g., finite difference methods, finite volume methods, semi-Lagrangian methods. Then we discuss the numerical schemes for the Convection-Diffusion equation, Burgers equation, Eulers equation and Navier Stokes equation. At the end of the course we also give an outlook to the microscopic modells, e.g. Boltzmann equation or Fokker-Planck equation, that are important to simulate small time- and spatial scales in fluid dynamics, e.g. turbulences or complex fluids.