Scattering of light by light is a fundamental process arising at the quantum level through vacuum fluctuations. This revised, concise book will explain how this quantum process can be described in terms of classical quantities. The description is derived from general principles such as causality, unitarity, Lorentz and gauge symmetries. The book introduces a rigorous formulation of these fundamental concepts, as well as their physical interpretation, in the context of light-by-light scattering. The book will also demonstrate how these principles emerge from quantum loop calculations of light-by-light scattering within the Standard Model (SM) of particle physics. The final chapter will give a survey of applications of the light self-interaction, ranging from non-linear optics to precision measurements of the muon anomaly and the dispersion of rays in cosmic microwave background (CMB), to the very recent discovery of light-by-light scattering at the Large Hadron Collider (LHC) at CERN.

This revised edition updates and extends the seven chapters of the first edition.

In particular, Chapter 3 is extended on the Kramers-Kronig relation to include another astrophysical application: dispersion by interstellar medium, which is very timely due to the Fast Radio Bursts (FRBs). Additionally, Chapter 7 will be revised extensively by including new sum rules for massive vector bosons, derived from doubly-virtual Compton scattering on spin-1 target (analogous to how it's done for spin ¿ in Chapter 5). This material is necessary to complete the subject of sum rules for spin-1 particles.

In overall, the text will be corrected and improved. New examples and figures will be included to aid reader's understanding. Comments of the author's students and colleagues, who are familiar with the first edition, will be taken into account.