Introduction and Examples. Overview of Inverse Problems / Michel Kern -- Examples of Inverse Problems / Michel Kern -- Linear Inverse Problems. Integral Operators and Integral Equations / Michel Kern -- Linear Least Squares Problems : Singular Value Decomposition / Michel Kern -- Regularization of Linear Inverse Problems / Michel Kern -- Nonlinear Inverse Problems. Nonlinear Inverse Problems : Generalities / Michel Kern -- Some Parameter Estimation Examples / Michel Kern -- Further Information / Michel Kern -- Appendices. Appendix 1: Numerical Methods for Least Squares Problems -- Appendix 2: Optimization Refreshers -- Appendix 3: Some Results from Functional Analysis