Lecture Notes in Physics

This book is a collection of pedagogical lecture notes on topics related to S-matrix theory. It presents recent progress in understanding the foundations of S-matrix theory from different perspectives, covering aspects such as analytic properties and infrared divergences, observables on time-folded contours and cosmological backgrounds, as well as lattice simulations and phenomenological applications in strongly-coupled QCD.The chapters are based on lectures given at the S-Matrix Marathon workshop, hosted in Princeton during the spring of 2024. The purpose is to provide a pedagogical introduction to the evolving ideas surrounding S-matrix theory and to highlight emerging directions in the field. This book is intended for junior researchers and advanced students who are interested in deepening their understanding of particle interactions.