Introduction and Basic Concepts: Ill-Posedness in inverse Problems, linear inverse problems, Classical Regularization Methods, Tikhonov Regularization, SVD, Projection Methods, Inverse Eigenvalue Problems, Besov space regularization, Inverse Scattering Problem, Variational Regularization Methods, Convex Regularization, Nonconvex Regularization, Statistical Inversion Theory, Nonlinear inverse problems, Inverse problems in imaging modalities and radar, applications in remote sensing, geoscience, biomedical, Computational inverse problems.