1. Introduction -- 2. Statistical distances -- 3. Continuous models -- 4. Measures of robustness and computational issues -- 5. The hypothesis testing problem -- 6. Techniques for inlier modification -- 7. Weighted likelihood estimation -- 8. Multinomial goodness-of-fit testing -- 9. The density power divergence -- 10. Other applications -- 11. Distance measures in information and engineering -- 12. Applications to other models.