This lecture starts with the basic concepts of fluids, flows and heat transfer. The components and properties as well as the limitations of numerical methods are then addressed, where different discretization approaches are examined. The fundamental principles of finite difference methods and finite volume methods are subsequently introduced followed by the investigation of various approaches for solving the linear equation systems. The time-marching methods for unsteady flow and heat transfer problems are surveyed, whereas the solution methods for the Navier-Stoke equations are demonstrated. The turbulent and compressible flow problems are also discussed together with the grid issues arising from complex geometries. The strategies for improving the computational efficiency and accuracy are reviewed. Hand-on hours of PDE solver platform and commercial CFD software are employed to the application of the principles of finite volume methods to the fluid dynamics and heat transfer problems.