“The book presents a nice summary of many interesting recent results on Tikhonov regularization for ill-posed and inverse problems … . The book … contains various interesting refinements and improvements. It is written in a very clear style, the material is well organized, and there is an extensive bibliography with useful comments on the most relevant literature. Hence, it is a very welcome addition to the modern standard references on ill-posed and inverse problems.” (Bangti Jin, zbMATH 1530.65007, 2024)

• Inverse problems, ill-posedness, regularization.- Variational source conditions yield convergence rates.- Existence of variational source conditions.- What are quadratic inverse problems?.- Tikhonov regularization.- Regularization by decomposition.- Variational source conditions.- Aren’t all questions answered?.- Sparsity and 1-regularization.- Ill-posedness in the l1-setting.- Convergence rates.

“The book presents a nice summary of many interesting recent results on Tikhonov regularization for ill-posed and inverse problems … . The book … contains various interesting refinements and improvements. It is written in a very clear style, the material is well organized, and there is an extensive bibliography with useful comments on the most relevant literature. Hence, it is a very welcome addition to the modern standard references on ill-posed and inverse problems.” (Bangti Jin, zbMATH 1530.65007, 2024)

• Inverse problems, ill-posedness, regularization.- Variational source conditions yield convergence rates.- Existence of variational source conditions.- What are quadratic inverse problems?.- Tikhonov regularization.- Regularization by decomposition.- Variational source conditions.- Aren’t all questions answered?.- Sparsity and 1-regularization.- Ill-posedness in the l1-setting.- Convergence rates.