In this project we investigate the strong coherent interaction of light and matter on the level of individual photons and individual atoms or atom-like systems. In particular, we explore large dipole moment superconducting artificial atoms and natural Rydberg atoms interacting with radiation fields contained in quasi-one-dimensional on-chip microwave frequency resonators. In these resonators individual photons generate field strengths that exceed those in conventional mirror based resonators by orders of magnitude and they can also be stored for long times. This allows us to reach the strong coupling limit of cavity quantum electrodynamics (QED) using superconducting electronic circuits, an approach known as circuit QED. In this project we explore novel approaches to perform quantum optics experiments in circuits. We develop techniques to generate and detect non-classical radiation fields using nonlinear resonators and chip-based interferometers. We also further advance the circuit QED approach to quantum information processing. The main objective of this project is to develop an interface between circuit and atom based realizations of cavity QED. In particular, we will couple Rydberg atoms to on-chip resonators. To achieve this goal we will first investigate the interaction of ensembles of atoms in a beam with the coherent fields in a continuous transmission line or a resonator. We will perform spectroscopic measurements of Rydberg atoms using field ionization detection and we will investigate detection schemes using the dispersive interaction with the resonator field. We will also explore the interaction of Rydberg atoms with chip surfaces in dependence on materials, temperature and geometry. Experiments will be performed from 300K down to millikelvin temperatures. We will realize and characterize on-chip traps for Rydberg atoms. Using trapped atoms we will explore their coherent dynamics in the vicinity of surfaces. Finally, we aim at investigating the single atom and single photon limit of these interactions. When realized this system will be used to explore the first quantum coherent interface between atomic and solid state qubits. This achievement will have impact on the development of quantum information processors and will contribute to the basic understanding of atom/solid interactions.