Quantum Integrability is a rich and highly cross-disciplinary subject, with fascinating mathematical structures and a wide spectrum of physical applications. It is the key tool for understanding critical properties of numerous quantum systems at and out of equilibrium, such as spin chains or the delta-function Bose gas (also known as the quantum non-linear Schrödinger equation). Long-standing problems such as the scaling limit of the Ising model in a magnetic field have been solved thanks to recent developments of integrable techniques. These developments in theoretical physics have been...