At the end of 1960 we made plans to write a monograph about the general principles of quantum field theory and their experimental implications. We intended primarily to give an account of the progress of the theory of dispersion relations since the appearance of the book of Bogolubov, Medvedev and Polivanov ([BMP]. As an introduction we wanted to include a review of the various approaches to axiomatic field theory. This introduction had to cover not only the formulation of Bogolubov, Medvedev and Polivanov, based on the apparatus of functional derivatives of the 5-matrix and the condition of microcausality, but also the field formulation associated with the names of Wightman, Haag, Lehmann, Symanzik, Zimmermann, and others. In the course of the work the tasks (and with them the size) of the introduction grew larger and larger, until eventually it developed into this book.