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.

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.