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“The author is to be commended for introducing a chapter on the gauge theory of fluid mechanics, which is quite ce in fluid mechanics books . . . the book can serve as an excellent introduction for graduate students in applied mathematics and physics who are interested in pursuing research in specific areas of fluid mechanics . . . One of the strengths of the book is its culmination in a detailed solution to all the problems.” Choice “This book contains an excellent basic presentation of theory, applications, and methods of solutions for various problems of classical and modern fluid dynamics.” Zentralblatt Math This textbook describes the fundamental “physical” aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics. It also emphasizes the dynamical aspects of fluid motions rather than the static aspects, illustrating vortex motions, waves, geophysical flows, chaos and turbulence. Beginning with the fundamental concepts of the nature of flows and the properties of fluids, the book presents fundamental conservation equations of mass, momentum and energy, and the equations of motion for both inviscid and viscous fluids. In addition to the fundamentals, this book also covers water waves and sound waves, vortex motions, geophysical flows, nonlinear instability, chaos, and turbulence. Furthermore, it includes the chapters on superfluids and the gauge theory of fluid flows. The material in the book emerged from the lecture notes for an intensive course on Elementary Fluid Mechanics for both undergraduate and postgraduate students of theoretical physics given in 2003 and 2004 at the Nankai Institute of Mathematics (Tianjin) in China. Hence, each chapter may be presented separately as a single lecture.