Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of new methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.