This text demonstrates an important interplay between abstract and concrete operator theory. The focus is on the investigation of a number of equations, which, while seemingly different, are all unified by the same idea: they are all realizations of some operator equations in Banach spaces. One permeating theme in these equations involves the role of the Fredholm property. The work is carefully written, is self-contained and covers a broad range of topics and results. Key ideas are developed in a step-by step approach, beginning with the required background material and culminating in the final chapters with state-of-the art topics. Experts in operator theory, integral equations and function theory as well as students in these areas will find open problems for further investigations. Good examples, bibliography and index make this text a valuable reference resource as well.