Multi-phase flows are part of our natural environment, including tornadoes, typhoons, air and water pollution and volcanic activity as well as industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. This book contains theory, methods and practical experience in describing complex transient multi-phase processes in arbitrary geometrical configurations. This book provides a sy- stematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present first volume the fundamentals of multiphase dynamics are provided, in addition to various interactive multimedia demonstrations on an accompanying CD-ROM.