The first chapters of this book define the notion of analog computing and cover the early history of mechanical and electromechanical analog computers before focusing on the development and the basics of electronic analog computing elements and computers based on these. Two chapters give an introduction to the programming of analog computers with a number of detailed sample problems and solutions. These problems range from simple mass-spring-damper systems to predator-prey simulations and conformal mappings. The following chapters introduce the basic concepts of hybrid computers and digital differential analyzers, the latter of which offer an enormous potential for future applications based on field programmable gate arrays (FPGAs) or the like. The second half of the book is dedicated to an overview of typical applications of analog computers based on a comprehensive bibliography. The last chapter describes future prospects for the analog computing paradigm.