Part I. General Background: 1. Data assimilation: general background; 2. Probability and Bayesian approach; 3. Filters and smoothers; Part I.: Practical Tools: 4. Tangent linear and adjoint model; 5. Automatic differentiation; 6. Numerical minimization process; Part III. Methods and Issues: 7. Variational data assimilation; 8. Ensemble and hybrid data assimilation; 9. Coupled data assimilation; 10. Dynamics and data assimilation; Part IV. Applications: 11. Sensitivity analysis and adaptive observation; 12. Satellite data assimilation; Index.