1. Introduction.- 1.1 Overview of CP Violation Without Strangeness.- 1.2 The Neutron Electric Dipole Moment: Early History.- 1.3 Molecular Electric Dipole Moments and CP Violation.- 1.4 T-Odd Effects Without CP Violation.- 1.4.1 Can an Unstable Particle Have a Dipole Moment?.- 1.4.2 Spurious EDM Effect Due to Nuclear Anapole Moment.- 2. Kinematics of Discrete Symmetries.- 2.1 CPT Theorem: Intuitive Approach.- 2.2 T-Even and T-Odd Electromagnetic Multipole Moments.- 2.3 General Structure of Four-Fermion Operators.- 3. General Features of EDM Experiments.- 3.1 Interaction of an EDM with an Electric Field.- 3.1.1 Sensitivity Limit Due to the Uncertainty Principle.- 3.1.2 Ramsey's Method of Separated Oscillatory Fields.- 3.1.3 Linewidth and Sensitivity with Separated Oscillatory Fields.- 3.2 Ground State Optical Pumping and Detection of Atomic Polarization.- 3.2.1 Atomic Spin Magnetometers.- 3.3 Electric Fields and Coherence Times in Various Systems.- 3.3.1 Electric Fields in Vacuum.- 3.3.2 Electric Fields in Gases.- 3.3.3 Electric Fields in Liquids.- 3.3.4 Electric Fields in Solids.- 3.3.5 Coherence Times for Various Systems.- 3.4 Magnetic Field Control and Generation.- 3.4.1 Field Stability and Homogeneity Requirements.- 3.4.2 Magnetic Shields.- 3.4.3 Field Generation.- 3.5 Systematic Effects.- 3.5.1 Leakage Current Effects.- 3.5.2 Problems Related to Polarizability and Electric Quadrupole Moments.- 3.5.3 The v × E Problem.- 4. The Search for the Neutron EDM.- 4.1 Properties of the Neutron.- 4.2 Interaction of Neutrons with Matter.- 4.2.1 Neutron Polarization.- 4.2.2 Production and Moderation of Neutrons.- 4.2.3 Transport of Cold Neutrons.- 4.3 Neutron Beam EDM Experiments.- 4.3.1 The Oak Ridge Experiment of 1950.- 4.3.2 The Oak Ridge Experiment of 1967.- 4.3.3 The Crystal Scattering Experiment of 1967.- 4.3.4 Pendellösung Fringes.- 4.3.5 Neutron Beam Experiments, 1968-1973.- 4.3.6 The Institut Laue-Langevin (ILL) Experiment of 1977.- 4.4 Ultracold Neutrons.- 4.4.1 Sources of Ultracold Neutrons.- 4.5 Neutron EDM Measurements with Stored Ultracold Neutrons.- 4.5.1 Present Limits for the Neutron EDM.- 4.5.2 Stored UCN EDM Experiment at the Institut Laue-Langevin.- 4.5.3 UCN EDM Experiment at the VVR-M Reactor, Petersburg Nuclear Physics Institute.- 4.5.4 The 199Hg Comagnetometer UCN Experiment.- 4.6 The Future: Superfluid He Neutron EDM with a 3He Comagnetometer.- 4.6.1 The Production of UCN in Superfluid 4He.- 4.6.2 Superfluid 4He Neutron EDM Search with a 3He Comagnetometer.- 4.6.3 Dressed Spin Magnetometry.- 4.6.4 Analysis of the Dressed Spin System and Systematic Effects.- 4.7 Comparison of Experimental Techniques.- 5. Theoretical Predictions for Neutron and Electron Dipole Moments.- 5.1 The CP-Violating ? Term in Quantum Chromodynamics.- 5.2 Predictions of the Standard Model for Dipole Moments.- 5.3 Spontaneous CP Violation in the Higgs Sector.- 5.4 Phenomenological Approach.- 6. EDM Experiments with Paramagnetic Atoms.- 6.1 The Shielding Problem.- 6.2 Enhancement of the Electron EDM in Paramagnetic Atoms.- 6.3 Overview of Paramagnetic Atom Experiments.- 6.4 The Cs EDM Experiment.- 6.5 The T1 EDM Experiment.- 6.6 Future Prospects for Improving the Electron EDM Limit.- 6.7 EDM Limits of Some Other Elementary Particles.- 6.7.1 The Proton.- 6.7.2 The Neutrino.- 6.7.3 The Muon.- 6.7.4 The ?0 Hyperon.- 6.7.5 The ? Lepton.- 7. EDM Experiments with Diamagnetic Atoms.- 7.1 Shielding in the 1S0 System.- 7.2 The 129Xe EDM Experiment.- 7.3 The 199Hg EDM Experiment.- 7.4 3He - 129Xe Comparison.- 8. Atomic Calculations.- 8.1 Wave Function of an Outer Electron at Short Distances.- 8.2 The Electron EDM in Paramagnetic Heavy Atoms.- 8.3 CP-Odd Electron-Nucleon Interaction.- 8.3.1 CP-Odd Mixing of Atomic Levels.- 8.3.2 Paramagnetic Atoms.- 8.3.3 Diamagnetic Atoms.- 8.3.4 Summary of the Constants K1,2,3.- 8.4 Electron EDM in Diamagnetic Atoms.- 8.5 CP-Odd Nuclear Moments.- 8.5.1 The Schiff Moment.- 8.5.2 Magnetic Quadrupole Moment.- 9. T Violation in Molecules.- 9.1 Enhancement of an Applied Field by a Polar Molecule.- 9.2 TIF Beam Experiments.- 9.3 What Have We Learned from the TIF Experiment?.- 9.4 Paramagnetic Molecules.- 9.5 What Will Be Gained from Experiments with Paramagnetic Molecules?.- 10. CP-Odd Nuclear Forces.- 10.1 CP-Odd Mixing of Opposite-Parity Nuclear Levels.- 10.2 Nuclear Moments Induced by T- and P-Odd Potentials.- 10.3 Enhancement Mechanisms for T- and P-Odd Nuclear Multipoles.- 10.4 Theoretical Predictions and Implications.- 11. What Do We Really Know About T -Odd, but P-Even Interactions?.- 11.1 Long-Range Effects.- 11.2 TOPE Fermion-Fermion Interactions.One-Loop Approach.- 11.3 TOPE Fermion-Fermion Interactions.Two-Loop Approach.- 11.4 Conclusions on TOPE eN and NN Interactions.- 11.5 T-Odd ? Decay Constants.- References.

Electric dipole moments (EDMs) have interested physicists since 1950, when it was first suggested that there was no experimental evidence that nuclear forces are symmetric under parity (P) transformation. This question was regarded as speculative because the existence of an EDM, in addition to P violation, requires a violation of time-reversal (T) symmetry. In 1964 it was discovered that the invariance under CP transformation, which combines charge conjugation (C) with parity, is violated in K-meson decays. This provided a new incentive for EDM searches. Since the combined operations of CPT are expected to leave a system invariant, breakdown of CP invariance should be accompanied by a violation of time-reversal symmetry. Thus there is a reason to expect that EDMs should exist at some level. The original neutron EDM experiments were later supplemented with checks of T invariance in atoms and molecules. These investigations are pursued now by many groups. Over the years, the upper limit on the neutron EDM has been improved by seven orders of magnitude, and the upper limit on the electron EDM obtained in atomic experiments is even more strict.