Free and moving boundary problems occur in such varied subjects as hydrology, heat flow, metallurgy, molecular diffusion, flame propagation, steel and glass production, and oil drilling and mathematical finance. This book presents a comprehensive account of the mathematical formulation of such problems and many new methods of solution. Computer methods, which allow multi-dimensional, multi-phase practical problems to be solved, are discussed. This book was written because of the upsurge of interest and research in this field. It bridges the gap between the various interested parties (including mathematicians, numerical and financial analysts, hydrologists, mechanical and chemical engineers, soil scientists, molecular biologists, physicists, metallurgists, and material scientists). The examples given are drawn from a variety of these fields. "...a broad but detailed account on mathematical and numerical methods for free and moving boundary problems that will be accessible to researchers both in the applied sciences and in applied mathematics.", C M Elliot, SIAM, Dec. 1988.