Introduction to localization in quantum field theory

Authors: Vasily Pestun and Maxim Zabzine Preprint Number: UUITP-22/16 This is the introductory chapter to the volume. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major applications of the localization calculations for supersymmetric theories. We explain the focus of the present volume.