This book treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and numerical analysis of Navier-Stokes equations; and turbulence and turbulence models used in simulations. Each chapter on theory is followed by a numerical analysis chapter that expands on the theory. The chapters contain numerous exercises. Introduction to the Numerical Analysis of Incompressible Viscous Flows provides the foundation for understanding the interconnection of the physics, mathematics, and numerics of the incompressible case, which is essential for progressing to the more complex ?ows not addressed in this book (e.g., viscoelasticity, plasmas, compressible ?ows, coating ?ows, ?ows of mixtures of ?uids, and bubbly ?ows). With mathematical rigor and physical clarity, the book progresses from the mathematical preliminaries of energy and stress to ?nite element computational ?uid dynamics in a format manageable in one semester.