Inverse problems is a class of mathematical and scientific challenges focused on determining the unknown causes, parameters, or properties of a system from measurements of its observable effects. This field investigates how to infer underlying models or inputs given observed outputs, often confronting issues such as non-uniqueness or instability of solutions (ill-posedness), which necessitate specialized analytical and computational techniques like regularization. Their significance lies in providing the foundational framework for interpreting experimental data, reconstructing images, and characterizing systems across diverse scientific, engineering, and medical disciplines.