Nonperturbative quantum field theory means the evaluation and investigation of quantum field theory be yond perturbation theory, andincludes a wide range o fp rob lems. It has been one oft he most fascinating topics of theoretical physical research in the past few decades and, in addition, it is closely linked with the investigation ofthe structure ofmatter. That isw hy an enormous number of papers has been de voted tot he treatment oft hese problems, and it would go beyond the scope of this preface - and even oft he whole book - to give areview of these developments. Thus we confine ourselves to referring to some modern books on quantum field theory where these topicsare treated; for instance, the books by Weinberg [Wein 95], [Wein 96], Dobado, Gomez Nicola, Marotoand Pelaez [Dob9 7]a nd Latal and Schweiger [Lat 97], and where further references canb e found. But summarizing the results obtained so far in this regard one cans ee that inspite ofg reat efforts there is still need of improvement and further progress.