This book is intended as a textbook for a first course in computational fluid dynamics and will be of interest to researchers and practitioners as well. It emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. The linear convection and diffusion equations are used to illustrate concepts throughout. The chosen approach, in which the partial differential equations are reduced to ordinary differential equations, and finally to difference equations, gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.