  The Jaynes-Cummings (JC) model has been at the forefront of quantum optics
for almost six decades to date, providing one of the simplest yet intricately
nonlinear formulations of light-matter interaction in modern physics. Laying
most of the emphasis on the omnipresence of the model across a range of
disciplines, this monograph brings up the fundamental generality of its
formalism, looking at a wide gamut of applications in specific physical systems
among several realms, including atomic physics, quantum optics, solid-state
physics and quantum information science. When bringing the various pieces
together to assemble our narrative, we have primarily targeted researchers in
quantum physics and quantum optics. The monograph also comprises an accessible
introduction for graduate students engaged with non-equilibrium quantum phase
transitions, quantum computing and simulation, and quantum many-body physics.
In that framework, we aim to reveal the common ground between physics and
applications scattered across literature and different technological
advancements. The exposition guides the reader through a vibrant field
interlacing quantum optics and condensed-matter physics. All sections are
devoted to the strong interconnection between theory and experiment,
historically linked to the development of the various modern research
directions stemming from JC physics. This is accompanied by a comprehensive
list of references to the key publications that have shaped its evolution since
the early 1960s. Finally, we have endeavored to keep the presentation of such a
multi-sided material as concise as possible, interspersing continuous text with
various illustrations alongside an economical use of mathematical expressions.
