Data assimilation for the geosciences : from theory to application Chapter 1. Introduction Chapter 2. Overview of Linear Algebra Chapter 3. Univariate Distribution Theory Chapter 4. Multivariate Distribution Theory Chapter 5. Introduction to Calculus of Variation Chapter 6. Introduction to Control Theory Chapter 7. Optimal Control Theory Chapter 8. Numerical Solutions to Initial Value Problems Chapter 9. Numerical Solutions to Boundary Problems Chapter 10. Introduction to Semi Langrangian Advection Methods Chapter 11. Introduction to Finite Element Modeling Chapter 12. Numerical Modeling of the Sphere Chapter 13. Tangent Linear Modeling and Adjoints Chapter 14. Observations Chapter 15. Non variational Sequential Data Assimilation Methods Chapter 16. Variational Data Assimilation Chapter 17. Subcomponents of Variational Data Assimilation Chapter 18. Observation of Space Variation Data Assimilation Methods Chapter 19. Kalman Filter and Smoother Chapter 20. Ensemble Based Data Asssimilation Chapter 21. Non Gaussian Variational Data Assimilation Chapter 22. Markov Chain Monte Carlo and Particle Filter Methods Chapter 23. Applications of Data Asssimilation in the Geosciences Chapter 24. Solutions to Select Exercise Bibliography Index