In the course of the last twenty years, teaching and research in fluid mechanics has expanded considerably into the physics and chemistry communities, who in their turn developed new approaches to the teaching of this topic. These approaches are mainly oriented towards the comprehension offluids of different hierarchies, the development of various experimental tools, and explanations in terms of elementary physical mechanics. Physical Hydrodynamics presents this original approach for the first time. The elementary microscopic basics of the statistical theory of fluids is discussed,as are the classical aspects of deformation and pressure and the laws of conservation. The problem of Low-Reynolds-Number Flows will be addressed, its applications to suspensions and porous media explained. A discussion of the aspects of boundary layers, high-velocity flows and instabilitiesconclude this presentation of incompressible fluid hydrodynamics. The present book provides a thorough introduction into the topic from a primarily physical point of view and will be a useful textbook and reference work for graduate students, lecturers and researchers.