This is the first course in the year-long set of courses in computational fluid dynamics. Building blocks of CFD: elliptic, parabolic and linear wave equations. Explicit vs. implicit time stepping methods. Various methods to solve the linear and nonlinear wave equation gradually building up to the Euler equations for compressible flow. Von Neumann linear stability of the developed methods . Riemann solvers in the context of Godunov-like methods. The course involves many hands-on programming assignments and a course code project.