Interfacial Wave Theory of Pattern Formation : Selection of Dendritic Growth and Viscous Fingering in Hele Shaw Flow The stabiltiy mechanisms of a curved front and the pattern formation in dendrite growth and viscous fingering have been fundamental subjects in the areas of condensed matter physics materials science crystal growth and fluid mechanics for about half a century. This book studies interfacial instability and pattern formation in dynamic systems away from the equilibrium state. In particular it deals with the two prominent prototype systems: dendrite growth in solidification and viscous fingering in Hele Shaw flow. It elucidates the key problems step by step and systematically derives their mathematical solutions on the basis of the newly established interfacial wave theory. Finally it carefully examines these results by comparisons with the available experimental results. The unified asymptotic approach described in this book will be useful for investigation of pattern formation phenomena occurring in a much broader class of inhomogeneous dynamic systems. The results on global stability and selection mechanisms of pattern formation given in this book will be of particular interest to researchers. For the readers who are not familiar with this rapidly growing interdisciplinary field this book will be a stimulating and valuable introduction