The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results. Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces. Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics. Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained. This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field. Key Features: o Written by two experts in the subject, this is the first book that gives a comprehensive survey on the study of biharmonic submanifolds and maps o Includes detailed proofs of most important results and the relations among various directions in the study of the subject o It is useful to researchers who have been working on the subject or the related topics as well as to graduate students or new researchers who have an interest in studying the subject and the related topics since the book also provides basic knowledge and tools used in the study of biharmonic maps and submanifolds

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