Image registration is one of the fundamental tasks within image processing. It is required when one wants to combine information from multiple images, possibly acquired using different modalities, at different time points or from different subjects, or to compare or integrate the data obtained from different measures. The subject of this book is nonrigid image registration. In particular, the main focus of the book is on the application of fluid dynamics and mutual information (MI) and the comparison of two different similarity measures, i.e. mutual information and sum of squared differences (SSD). Numerical experiments show that fluid registration using SSD is ideal for mono-modal image registration, while fluid registration using MI does a better job in multi-modal image registration.