The key contribution of the approach to x-ray mammographic image analysis developed in this monograph is a representation of the non-fatty compressed breast tissue that we show can be derived from a single mammogram. The importance of the representation, called hint, is that it removes all those changes in the image that are due only to the particular imaging conditions (for example, the film speed or exposure time), leaving just the non-fatty interesting' tissue. Normalising images in this way enables them to be enhanced and matched, and regions in them to be classified more reliably, because unnecessary, distracting variations have been eliminated. Part I of the monograph develops a model-based approach to x-ray mammography, Part II shows how it can be put to work successfully on a range of clinically-important tasks, while Part III develops a model and exploits it for contrast-enhanced MRI mammography. The final chapter points the way forward in a number of promising areas of research. Audience: This book has been written for a wide readership, including medical image analysts, medical physicists, radiologists, breast surgeons, and research students. The mathematics and algorithms have been relegated to boxes so that the book can be read and understood even if the mathematical detail is skipped. Large parts of the monograph will be of interest to clinicians generally and to patients.