Viscous flow crops up in many real-life situations such as aerodynamics and lubrication, and because of its universality it is a paradigm for the application of mathematics to the real world. This book is a coherent account of the ways in which mathematics can both give insight into viscous flow and suggest analogies and implications for other branches of applied mathematics. The authors place particular emphasis on the unification brought about by the use of asymptotic analysis and scaling properties and the use of everyday observations from the real world (especially industry) to illustrate the theory. The book is aimed at final-year undergraduate and beginning graduate students in applied mathematics, physics, and engineering courses on fluid flow.