This main purpose of this book is to present the basic theory of well-posed linear systems in a form which makes it available to a larger audience, thereby opening up the possibility of applying it to a wider range of problems. Up to now the theory has existed in a distributed form, scattered between different papers with different (and often noncompatible) notation. For many years this has forced authors in the field (myself included) to start each paper with a long background section to first bring the reader up to date with the existing theory. Hopefully, the existence of this monograph will make it possible to dispense with this in future.

My personal history in the field of abstract systems theory is rather short but intensive. It started in about 1995 when I wanted to understand the true nature of the solution of the quadratic cost minimization problem for a linear Volterra integral equation. It soon became apparent that the most appropriate setting was not the one familiar to me which has classically been used in the field of Volterra integral equations (as presented in, e.g., Gripenberg et al. [1990]). It also became clear that the solution was not tied to the class of Volterra integral equations, but that it could be formulated in a much more general framework. From this simple observation I gradually plunged deeper and deeper into the theory of well-posed (and even non-well-posed) linear systems.