This textbook presents essential methodology for physicists of the theory and applications of fluid mechanics within a single volume. Building steadily through a syllabus, it will be relevant to almost all undergraduate physics degrees which include an option on hydrodynamics, or a course in which hydrodynamics figures prominently. This book introduces the core ideas of fluid mechanics using both theoretical and experimental methods. The text presents a logical assembly of important ideas, approaches and specialist applications in one self-contained volume. Its unique focus combines the fundamental topics of fluid mechanics, such as equations of motion, ideal flows, viscous effects and turbulent flow. Engineering topics such as heat transfer and aerodynamics are briefly introduced. Full treatments of both incompressible and compressible flows are included. There is also a section of problems and worked solutions. The extensive material in this comprehensive text serves as a thorough background in fluid mechanics and the area of compressible flows. Introductory Fluid Mechanics for Physicists and Mathematicians is a valuable resource for physicists and mathematicians, and for undergraduate and postgraduate students in both disciplines. Readers will gain a strong working knowledge of fluid mechanics and a detailed understanding which will allow them to contribute to the new and evolving areas of study that are constantly emerging in this area.