List of figures; List of algorithms; Notation; Preface; Part I. Basic Methods and Algorithms for Data Assimilation: 1. Introduction to data assimilation and inverse problems; 2. Optimal control and variational data assimilation; 3. Statistical estimation and sequential data assimilation; Part II. Advanced Methods and Algorithms for Data Assimilation: 4. Nudging methods; 5. Reduced methods; 6. The ensemble Kalman filter; 7. Ensemble variational methods; Part III. Applications and Case Studies: 8. Applications in environmental sciences; 9. Applications in atmospheric sciences; 10. Applications in geosciences; 11. Applications in medicine, biology, chemistry, and physical sciences; 12. Applications in human and social sciences; Bibliography; Index.