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.