This book is a serious introduction to fluid dynamics with rigorous mathematical analysis of fundamental topics. It consists of 29 chapters, which are grouped into five sections. A general introduction to analytical fluid dynamics is given in Sections I, III and IV, while more specific topics, namely advanced gas dynamics and boundary-layer theory are discussed in Sections II and V, respectively.

Governing equations are established in Section I, with tensor notation employed and used throughout the book. Also notable are exercise problems at the end of each chapter which often build up on what have been discussed in the text and also introduce realistic applications. Useful formulae are neatly summarised in 18 sections of appendix. This book will be particularly useful for those interested in compressible flows, as Section II and the latter part of Section V are heavily focused on those. This is a welcome addition to the audience of The Aeronautical Journal, as classic textbooks on theoretical fluid dynamics, such as that of G.K. Batchelor, often focus on incompressible flows only.

The author's remarkable achievement is that mathematical methods, especially advanced linear algebra and transformation theories are seamlessly introduced while discussion is focused on physics of fluid problems. Although there are many textbooks available that survey mathematical methods commonly used in science and engineering, fluid mechanics examples used in those books are often out of the context.

Therefore, this book is recommended not only to fluid mechanics scientists and engineers who want to establish firm theoretical foundation but also to applied mathematicians who wish to apply mathematical methods to fluid mechanics problems. Readers would need some proficiency in advanced engineering mathematics; therefore, it will be more suitable for graduate students and professionals.