Theory of the energy levels and precise two-photon spectroscopy of atomic hydrogen and deuterium

In the last few years significant progress has been achieved both in the experimental technique and the theoretical methods for the determination of the energy levels of simple hydrogenic systems. We review recent two-photon spectroscopic measurements performed in Garching and the relevant theoretical predictions for the hydrogen energy levels. Good agreement is achieved when all theoretical contributions are included, showing the importance of recently calculated higher order corrections. (Author)