This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.Preface On the Contact Topology and Geometry of Ideal Fluids (Robert Christ) Shock Reflection in Gas Dynamics (Denis Serre) The Mathematical Theory of the Incompressible Limit in Fluid Dynamics (Steven Schochet) Local Regularity Theory of Navier-Stokes Equations (Gregory Seregin) On the Influence of the Earth's Rotation on Geophysical Flows (Isabelle Gallagher and Laure Saint-Raymond) The Foundations of Oceanic Dynamics and Climate Modelling (George R. Sell) Mathematical Properties of the Solutions to the Equations Governing the Flow of Fluids with Pressure and Shear Rate Dependent Viscosities (Josef M?lek and K.R. Rajagopal) Navier-Stokes System in Domians with Cylindrical Outlets to Infinity (Konstantin Pileckas) Periodic Homogenization Problems in Incompressible Fluid Equations (Carlos Conca and M. Vanninathan) Author Index Subject Index