"Feasibility and Infeasibility in Optimization" is a specialized book that focuses on practical algorithms for assessing feasibility and infeasibility in optimization. It is divided into three main parts: The first part addresses algorithms for quickly determining feasibility, including new approaches for complex problems such as nonlinear and mixed-integer programs. The second part concentrates on the analysis of infeasibility by isolating minimal infeasible or maximal feasible constraints, or by finding the best solutions to resolve infeasibility. The third part presents surprising applications in areas such as classification, computational biology, and medicine. Additionally, connections to constraint programming are highlighted. The book is aimed at researchers, students, and practitioners in the applied sciences who deal with optimization problems, and it seeks to provide a deep understanding of the methods to enable the immediate application of existing algorithms and software.