Note: Intro -- The Hydrogen Atom -- Foreword -- Preface -- Table of Contents -- List of Contributing Participants -- Introduction to Simple Atoms -- 1 Historica Remarks -- 2 Precision Physics of Simple Atoms -- 3 Studying the Simple Atoms -- 3.1 Hydrogen and deuterium (see [6,7] and Part VI) -- 3.2 Muonium and Positronium (see [12,13] and Part VII) -- 3.3 Muonic Atoms and Nuclear Structure (see Part VIII) -- 3.4 Nuclear-Structure Independent Differences -- 3.5 Fine Structure in Helium (see [23] and Part VI) -- 3.6 Few-Electron Ions (see [26,27] and Part XI) -- 3.7 Medium-Z Physics (see [26,27] and Part XI) -- 3.8 Higher-Order Corrections -- 3.9 Bound State QED -- 3.10 Exotic Atoms (see [35,36] and Part IX) -- 3.11 Antihydrogen and CPT Violation (Part IX) -- 3.12 Exotic Events -- 3.13 Variation of Constants (Part X) -- 3.14 Precision Frequency Metrology ([38] and Part X) -- 3.15 Determination of Fundamental Constants ([39,40] and Part X) -- 4 About This Publication -- Acknowledgements -- References -- Precision Spectroscopy of Atomic Hydrogen -- 1 Introduction -- 2 The Hydrogen 1S -2S Transition -- 2.1 Hydrogen 1S -2S Two-Photon Spectroscopy in an Atomic Beam -- 2.2 Theoretical Line Shape Model -- 2.3 Optical Lamb Shift Measurements -- 2.4 Absolute Measurements of the 1S -2S Transition Frequency in Atomic Hydrogen -- 2.5 1S-2S Isotope Shift and the Deuteron Structure Radius -- 3 Spectroscopy of the2S-nS and 2S-nD Transitions -- 3.1 Method -- 3.2 Optical Frequency Measurements in Paris -- 3.3 Comparison of the 1S-3S and 2S-6 S/D Transitions -- 4 Determination of the Rydberg Constant and Lamb Shifts -- 4.1 Rydberg Constant -- 4.2 Lamb Shifts -- 5 Conclusion and Prospects -- References -- Ultracold Hydrogen -- 1 Introduction -- 2 Ultracold Hydrogen Research at MIT -- 2.1 The Road to Bose-Einstein Condensation -- 2.2 Two-Photon 1S-2S Spectroscopy. , 2.3 Bose-Einstein Condensation -- 2.4 High Resolution Spectroscopy in Ultracold Hydrogen -- Acknowledgments -- References -- Review of High Precision Theory and Experiment for Helium -- 1 Introduction -- 2 Principal Effects -- 3 Nonrelativistic Wave Functions -- 3.1 Recent Advances -- 4 Asymptotic Expansions -- 5 Relativistic Corrections -- 6 Quantum Electrodynamic Corrections -- 6.1 Electron-Nucleus Terms -- 6.2 Electron-Electron Terms -- 6.3 Higher Order Terms -- 7 Comparison with Experiment -- 7.1 Measurement of the Fine Structure Constant -- 7.2 Applications to Lithium -- 8 Concluding Remarks -- Acknowledgements -- References -- Spectroscopy of the Muonium Atom -- 1 Introduction -- 2 Muonium Formation -- 3 Ground State Hyperfine Structure -- 4 1s-2s Energy Interval -- 5 Connection to a New Measurement of the Muon Magnetic Anomaly -- 6 Muonium-Antimuonium Conversion -- 7 Long Term Future Possibilities -- 8 Conclusions -- 9 Acknowledgements -- References -- Experimental Tests of QED in Positronium: Recent Advances -- 1 Introduction -- 2 Decay Rates -- 2.1 Para-Positronium Decay Rate λ (1^1 S_0) -- 2.2 Ortho-Positronium Decay Rate λ (1^3 S_1) -- 3 Energy Level Intervals -- 3.1 Ground State Interval -- 3.2 Rydberg Interval -- 3.3 Intervals in the n=2 and 3 excited states -- 4 Summary and Conclusions -- References -- A New Type of Frequency Chain and Its Application to Fundamental Frequency Metrology -- 1 Introduction -- 2 Kerr-Lens Mode-Locked Lasers -- 3 Femtosecond Frequency Combs -- 4 Spectral Broadening by Self-Phase Modulation -- 5 Photonic Crystal Fibers -- 6 Phase-Locking the Frequency Comb -- 7 Self-calibrated Optical Combs: Absolute Optical Frequencies -- 8 Accuracy Tests of the fs Laser Comb Approach -- 9 The Fine Structure Constant α -- 10 Conclusion -- Acknowledgement -- References -- Fundamental Constants and the Hydrogen Atom*. , 1 Introduction -- 2 1998 Least Squares Adjustment -- 3 Electron Magnetic Moment Anomaly -- 4 Rydberg Constant -- 4.1 Theory Relevant to the Rydberg Constant -- 4.2 Self Energy -- 4.3 Two-Photon Corrections -- 4.4 Finite Nuclear Size -- 4.5 Total Energy and Uncertainty -- 4.6 Result of LSA for the Rydberg Constant -- 5 Conclusion -- References -- Present Status of g − 2 of Electron and Muon -- 1 Introduction -- 2 Electron Magnetic Moment Anomaly -- 3 Muon Magnetic Moment Anomaly -- 4 Improving the alpha^4 Term of the Electron g-2 -- 5 Concluding remarks -- Acknowledgments -- Appendix: VEGAS and Feynman Integral -- References -- Laser Spectroscopy of Hydrogen-Like and Helium-Like Ions -- 1 Introduction -- 2 Fast-Beam Laser Resonance Technique -- 2.1 Signal Formation -- 2.2 Co-linear Geometry and Kinematic Compression -- 2.3 Determination of the Beam Velocity: Doppler-tuned Spectroscopy with Co- and Counter-Propagating Laser Beams -- 2.4 Wavefront Curvature Effects -- 2.5 Alternatives to the Beam-Foil Technique -- 3 Hydrogen-like Ions -- 3.1 Lamb Shift -- 3.2 Experimental Considerations -- 3.3 Lamb Shift Measurements in F^8+, P^14+, S^15+ and Cl^16+ -- 3.4 Future Prospects for Laser Lamb Shift Measurements -- 3.5 Ground-state Hyperfine Structure of High-Z Hydrogen-like Ions -- 4 Helium-like Ions -- 4.1 Experimental Considerations -- 4.2 2^3 S_1 - 2^3 P_J Transitions in Li^+ ,Be^2+ and B^3+ -- 4.3 2^1 S_0 - 2^3 P_1, 2^3 P_0 Intercombination Transitions in N^5+ -- 4.4 2^3 P_J - 2^3 P_J' Fine Structure Transitions in F^7+ and Mg^10+ -- 4.5 Future Prospects -- 5 Conclusions -- Acknowledgments -- References -- The g Factor of Hydrogenic Ions: A Test of Bound State QED -- 1 Introduction -- 2 Summary of Theory -- 3 Experiment -- 4 Results -- 5 Future Prospects -- 5.1 Electron Mass -- 5.2 Fine Structure Constant -- 5.3 Electron Binding Energies. , 5.4 Nuclear Magnetic Moments -- 5.5 Lithium-like Ions -- Acknowledgements -- References -- Elementary Relativistic Atoms -- 1 Introduction -- 2 Atom consisting of π and µ mesons -- 2.1 A_pi mu properties -- 2.2 Observation of A_πµ -- 2.3 Measurement of the A_πµ formation rate in K^0_L decay -- 3 Ultrarelativistic positronium atoms (A_2e) -- 3.1 Source of the ultrarelativistic A_2e and their quantum numbers -- 3.2 Superpenetration of ultrarelativistic atoms -- 3.3 Time-of-formation effects in production of ultrarelativistic A_2e -- 3.4 Observation of ultrarelativistic positronium and measurement of the branching ratio for the pi°-mesons decay... -- 3.5 Measurement of the total cross section for interaction of ultrarelativistic positronium atoms with carbon. -- 4 π^+ π^- atom -- 4.1 A_2π production and lifetime -- 4.2 A_2π detection method and setup description -- 4.3 Data processing -- 4.4 Approximation procedure for the pi^+ pi^ - pair distribution A_2pi number obtaining -- 4.5 Status of A_2π investigation at CERN -- 4.6 A_piK as a source of model-independent data on piK S-wave scattering lengths -- Acknowledgements -- References -- Antiprotonic Helium - An Exotic Hydrogenic Atom -- 1 Introduction -- 2 Unique Facets of Antiprotonic Helium -- 3 Advanced Theories -- 4 Laser Spectroscopy of Antiprotonic Helium -- 5 Precise Determination of Transition Energies -- 6 Chemical Physics Aspects -- 6.1 State Dependent Lifetime Shortening -- 6.2 Pressure Shifts of Resonance Lines -- 6.3 Quenching with H_2 Admixtures -- 6.4 Hydrogen-Assisted Inverse Resonances and Individual Quenching Rates -- 7 Hyperfine Structure -- 8 The Future -- References -- Towards a Precise Measurement of the He+ 2S Lamb Shift -- 1 Introduction -- 2 Overview of Lamb Shift Calculations -- 3 The Experimental Method -- 3.1 The UV Ligh Source -- 3.2 The Interaccion Region. , 3.3 The He^+2S Ion Source and Beam -- 3.4 Metastable Detection -- 3.5 The Reference Laser System -- 3.6 Detection of the Two-Photon Transition -- 4 Conclusion -- 5 Acknowledgments -- References -- High Precision Measurements on Helium at 1083 nm -- 1 Helium and Fundamental Physics -- 2 Fine Structure of the Helium 2^3 P Level: Experiments -- 2.1 The Florence Experiment -- 2.2 State of the Art of the 2^3 P Helium Splittings -- 3 Hyperfine Iodine Transitions at 541 nm: a New Frequency Reference for Helium Spectroscopy -- 4 Conclusions and Final Remarks -- Acknowledgments -- References -- Absolute Frequency Measurement of the 1S-3S Transition in Hydrogen -- Conclusion -- References -- 2s Hyperfine Structure in Hydrogen Atom and Helium-3 Ion -- 1 Introduction -- 2 Theory -- 2.1 Non-recoil limit -- 3 Present status of D21 theory -- 3.1 Old theory and recent progress -- 3.2 Our results -- 4 Present status -- Acknowledgments -- References -- Three-Loop Slope of the Dirac Form Factor and the 1S Lamb Shift in Hydrogen -- 1 Introduction -- 2 Strategy of the calculation -- 3 Basics of the program -- 4 Results -- 5 Acknowledgments -- References -- Radiative Decay of Coupled States in an External dc Field -- 1 Theory and results -- References -- Atomic Interferometer and Coherent Mixing of 2S and 2P States in the Hydrogen Atom -- 1 Atomic interferometer method -- 2 Discussions -- References -- Ground State Energy of the Helium Atom -- 1 Introduction -- 2 Framework of the calculation -- 3 Soft Scale Contributions -- 3.1 Irreducible corrections -- 3.2 Reducible Corrections -- 3.3 Total soft scale contribution -- 4 Hard Scale Contributions -- 4.1 Radiative Recoil Correction -- 4.2 Radiative Corrections -- 4.3 Pure Recoil Correction -- 5 Conclusion -- Acknowledgments -- Appendix -- References -- Two-Loop Corrections to the Decay Rate of Orthopositronium. , 1 Introduction.