"The Diffuse Interface Approach in Materials Science" is a specialized book that focuses on the analysis of inhomogeneous systems characterized by well-defined phases and their interfaces. It addresses the dynamics of phase transitions and the growth of phases under nonequilibrium conditions. Topics covered include phase separation, dendritic solidification, and the associated physical phenomena. The book provides a detailed description of the theoretical foundations and mathematical models used to analyze these processes. It is aimed at professionals and students in materials science who wish to gain a deeper understanding of the Diffuse Interface method and its applications in materials research. The author, Heike Emmerich, draws on her expertise in theoretical physics and materials science to make complex concepts accessible and to highlight the relevance of these approaches in modern research.