Prof. Newman is considered one of the great chemical engineers of his time. His reputation derives from his mastery of all phases of the subject matter, his clarity of thought, and his ability to reduce complex problems to their essential core elements. He is a member of the National Academy of Engineering, Washington, DC, USA, and has won numerous national awards including every award offered by the Electrochemical Society, USA. His motto, as known by his colleagues, is "do it right the first time." He has been teaching undergraduate and graduate core subject courses at the University of California, Berkeley (UC Berkeley), USA, since joining the faculty in 1966. His method is to write out, in long form, everything he expects to convey to his class on a subject on any given day. He has maintained and updated his lecture notes from notepad to computer throughout his career. This book is an exact reproduction of those notes. This book demonstrates how to solve for the velocity profile of the classic problems of fluid mechanics, starting with Navier-Stokes equation. It explains when it is appropriate to simplify a problem by neglecting certain terms through proper dimensional analysis. It covers concepts such as basic relations of fluid mechanics, microscopic interpretation of fluxes, concentrations and velocities in mixtures, multicomponent diffusion, entropy production and implications for transport properties, Lighthill's transformations, perturbation methods and the singular perturbation method, non-Newtonian fluids, natural convection, turbulent flow, and hydrodynamic stability. It presents numerous examples such as Stokes flow past a sphere, heat transfer in a pure fluid, flow to a rotating disk, mass transfer to a rotating disk, boundary layer on a flat plate, creeping flow past a sphere, mass transfer to the rear of a sphere, Graetz-Leveque problem, spin coating, and mass transfer in turbulent flow and turbulent boundary layers. It is as much a thesis on transport phenomena as it is in applied mathematics, and it amply arms any serious problem solver with the tools to address any problem.