Linear inverse problems and Tikhonov regularization Introduction to inverse problems Well posed ill posed and inverse problems Tikhonov regularization Compact operators and the singular value expansion Tikhonov regularization with seminorms Epilogue. Basic Hilbert space theory Sobolev spaces Inverse problems occur frequently in science and technology whenever we need to infer causes from effects that we can measure. Mathematically they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless there are methods for finding good approximate solutions. Linear Inverse Problems and Tikhonov Regularization examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems.