A NATO Advanced Study Institute (ASI) on High-Brightness Accelerators was held at the Atholl Palace Hotel, Pitlochry, Perthshire, Scotland, from July 13 through July 25, 1986. This publication is the Proceedings of the Institute. This ASI emphasized the basic physics and engineering of the rela­ tively new and fast-emerging field of high-brightness particle accelera­ tors. These machines are high- to very-high-current (amperes to hundreds of kiloamperes), modest-voltage (megavolt to tens of megavolts) devices, and as such are opposed to those historically used for high-energy physics studies (i.e., gigavolt and higher energies and rather low currents). The primary focus of the Institute was on the physics of the accelerator and the beam, including the dynamics, equilibria, and insta­ bilities of high-current beams near the space-charge limit; accelerator engineering techniques; and the applications of high-brightness beams in areas such as free-electron lasers, synchrotron-radiation sources, food processing, and heavy- and light-ion fusion. The Institute concentrated on bringing together several diverse but related communities which, we hope, benefited from this opportunity to interact: the North American activity in machine technology, engineer­ ing, and diagnostics with the strong European theoretical community; the basic beam physicists with the engineering technologists.