The book "Mathematical Models for Registration and Applications to Medical Imaging" offers a comprehensive analysis of the mathematical models that are significant for image registration in medical imaging. Image registration is a central topic in image processing that deals with determining suitable transformations between different datasets. These transformations can vary depending on the application and include, among others, Euler, rigid, plastic, and elastic deformations. The work highlights the challenges and solutions arising from the complexity of registration and discusses the need for efficient numerical realizations. Experts from industry and medicine contribute to the discussion of relevant applications and new mathematical technologies in this field. The topics covered range from the theory of partial differential equations to variational principles that are crucial for solving registration problems.