This book is based on a graduate course taught four times, once in French at the Université de Montréal and then three times in English at the Institut für Theoretische Physik, in Innsbruck, Austria, at the Center for Quantum Spacetime, Department of Physics, Sogang University, Seoul, Korea, and most recently, a part of it at the African Institute for Mathematical Sciences (AIMS), Cape Town, South Africa.

The course covered the contents of the magnificent Erice lectures of Coleman [31], “The Uses of Instantons”, in addition to several chapters based on independent research papers. However, it might be more properly entitled, “The Uses of Instantons for Dummies”. I met Sidney Coleman a few times, more than 30 years ago, and although I am sure that he was less impressed with the meetings than I was and probably relegated them to the dustbin of the memory, my debt to him is enormous. Without his lecture notes I cannot imagine how I would ever have been able to understand what the uses of instantons actually were. However, in his lecture notes, one finds that he also thanks and expresses gratitude to a multitude of eminent and great theoretical physicists of the era, indeed thanking them for “patiently explaining large portions of the subject” to him. Unfortunately, we cannot all be so lucky. Coleman's lecture notes are a work of art; it is clear when one reads them that one is enjoying a master impressionist painter's review of a subject, a review that transmits, as he says, the “awe and joy” of the beauty of the “wonderful things brought back from far places”. But then the hard work begins.

Hence, through diligent, fastidious and brute force work, I have been able, I hope, to produce what I believe is a well-rounded, detailed monograph, essentially explaining in a manner accessible to first- and second-year graduate students the beauty and the depth of what is contained in Coleman's lectures and in some elaborations of the whole field itself.