This book, published as Vol. 90 of the Frontiers in Physics series, is a most welcome introduction to the study of internal interfaces found in complex multicomponent systems. The material is presented in the form of a set of lecture notes with an introductory chapter containing a brief review of the statistical mechanics, differential geometry and hydrodynamics on a level appropriate for a proper understanding of later developments. In this respect the book is basically self-contained. It also contains worked-out examples and problems at the end of each chapter. The book is intended to reach a wide interdisciplinary audience of physicists, physical chemists, chemical engineers, and materials scientists, and presents an elegant and unifying introduction to the field of interfaces in multicomponent systems.