This book highlights a comprehensive and self-contained account of the physics of Rydberg atoms and their integration within the broader framework of cavity quantum electrodynamics (QED) and hybrid quantum systems. Rydberg atoms in cavities constitute a uniquely powerful and versatile platform for exploring strongly interacting quantum systems, where the combination of exaggerated atomic properties and engineered light&matter coupling enables access to physical regimes that are otherwise unattainable. With their exceptionally large electric dipole moments, long radiative lifetimes, and extreme sensitivity to external electric and magnetic fields, Rydberg atoms amplify the strength of interatomic interactions by several orders of magnitude compared to ground-state atoms. When placed within optical or microwave resonators, these properties are further enhanced through cavity quantum electrodynamics (QED), which provides precise control over the interaction between matter and confined electromagnetic fields. This integration allows the realization of deterministic quantum gates, scalable entanglement generation, and photonic nonlinearities at the level of single photons-capabilities that are at the core of quantum information science and next-generation quantum technologies.
 
Our central aim is to furnish the reader with both a foundational understanding of Rydberg physics and the advanced theoretical and technical tools required to contribute to the fast-growing research landscape. The exposition begins with the preparation and characterization of Rydberg states, including excitation techniques, radiative properties, and spectroscopic methods. It then systematically develops the key interaction mechanisms-such as dipole blockade, Förster resonances, and tunable long-range van der Waals and dipole&dipole couplings-that underpin many-body correlations and collective dynamics. These mechanisms form the basis for much of the remarkable physics observed in ensembles of Rydberg atoms. The narrative then shifts to the interplay between strong atomic interactions and the confined electromagnetic modes of resonators.