The possibility of the existence of permanent electric dipole moments (EDMs), which would be evidence of a breakdown of time-reversal symmetry, has been of interest to physicists for neary half a century. This question gained renewed interest with the discovery in 1964 of CP violation in the decay of the K0 meson. Experimental searches for EDMs have severely constrained the possible theories that describe the CP-violation. The fundamental physical theories put forward to describe the K0 system are described, and application to the calculation of EDMs of the electron, the neutron, atoms, and molecules is thoroughly reviewed. The theoretical description is embellished by a comprehensive review of the experimental seraches for EDMs, along with an overview of likely future experimental trends. The book represents the first complete and simultaneous description of both theoretical and experimental techniques related to the issues of EDMs. It is intended for advanced graduate students who want a solid introduction to the theoretical and experimental issues, and for workers in the field who want a comprehensive review and overview of current work.