This book is a dedicated collection of invited papers associated with ICIAM 2023. It features twelve contributions covering a broad spectrum of topics in applied and computational mathematics, ranging from mathematical modeling and algorithm development to diverse real-world applications.The contents include research on two-phase flows, fluid-structure interactions, and free boundary and interface problems. Each paper presents advances in mathematical modeling, analytical techniques, and computational methods, reflecting the depth and relevance of current research in these areas. This volume aims to serve as a valuable resource for researchers and practitioners working across disciplines where mathematics plays a central role in understanding and solving complex problems.