This second edition of Linear Operator Equations: Approximation and Regularization provides a modern, accessible, and student-friendly introduction to the theory and numerical treatment of linear operator equations, both well-posed and ill-posed.With rewritten and expanded proofs, a more consistent structure, and numerous new exercises and examples, the book offers clear pathways for learning approximation theory, regularization techniques, and applications of functional analysis to inverse problems. New topics include truncated singular value decomposition, generalized Tikhonov regularization with stabilizing operators, and a deeper treatment of discrete projection methods for operator equations.Designed for students and researchers alike, the book balances theoretical rigor with practical insights, making it a valuable resource for courses in numerical functional analysis, inverse problems, and operator theory, or for self-study by applied mathematicians, engineers, and computational scientists.A newly expanded bibliography, revised notation, and systematic numbering make this edition even more usable as a reference and teaching tool.