Scatering amplitudes in Gauge theory and gravity This book grew out of a need to have a set of easily accessible notes that introduced the basic techniques used in modern research on scattering amplitudes. In addition to the key tools such a review should collect some of the small results and intuitions the authors had acquired from their work in the eld and which had not reviously been exposed in the literature. As the authors quickly realized such an introduction would bring the reader only part of the way towards some of the most exciting topics in the eld so they decided to add a little extra material. While doing so and this took quite a while the authors remained in full and complete denial about writing a book. It was only at the end of process that they faced their worst fears: the review was becoming a book. You now hold the result in your hands. Because the authors were not writing a book they actually thoroughly enjoyed the work. Their hope is that you will enjoy it too and that you will nd it useful Providing a comprehensive pedagogical introduction to scattering amplitudes in gauge theory and gravity this book is ideal for graduate students and researchers. It offers a smooth transition from basic knowledge of quantum field theory to the frontier of modern research. Building on basic quantum field theory the book starts with an introduction to the spinor helicity formalism in the context of Feynman rules for tree level amplitudes. The material covered includes on shell recursion relations superamplitudes symmetries of N=4 super Yang Mills theory twistors and momentum twistors Grassmannians and polytopes. The presentation also covers amplitudes in perturbative supergravity 3D Chern Simons matter theories and color kinematics duality and its connection to gravity=(gauge theory)2. Basic knowledge of Feynman rules in scalar field theory and quantum electrodynamics is assumed but all other tools are introduced as needed. Worked examples demonstrate the techniques discussed and over 150 exercises help readers absorb and master the material