The proposed book will be a revision and update of the textbook entitled: "An Introduction to Computational Fluid Mechanics" by C. Y. Chow which was originally published in 1979. The original edition was written for senior undergraduate and first-year graduate students as well as professional engineers and researchers in the mechanical and aerospace industries. In the decades that have passed since this first edition was published the field of computational fluid dynamics has seen a number of changes in both the sophistication of the algorithms used but also advances in the computer hardware and software available. The proposed revision will incorporate the latest algorithms in the solution techniques and will support this by using numerous examples of applications to a broader range of industries from the original mechanical and aerospace disciplines to now include civil and biosciences. The computer programs will be updated and will include both Fortran 77 and MATLAB. The core of the text will also be expanded to include more up-to-date solution methods for the Navier-Stokes equations, including fractional step time-advancement, and pseudo-spectral methods. A solutions manual will be made available as well.