Multiphase systems dominate nearly every area of science and technology, and the method of volume averaging provides a rigorous foundation for the analysis of these systems. The development is based on classical continuum physics, and it provides both the spatially smoothed equations and a method of predicting the effective transport coefficients that appear in those equations. The text is based on a ten-week graduate course that has been taught for more than 20 years at the University of California at Davis and at other universities around the world. The theoretical foundations and the applications are included with each chapter, and detailed solutions for all problems are available from the author. The course has attracted participants from chemical engineering, mechanical engineering, civil engineering, hydrologic science, mathematics, chemistry and physics.