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An introductory review of the linear ion trap is given, with particularregard to its use for quantum information processing. The discussion aims tobring together ideas from information theory and experimental ion trapping, toprovide a resource to workers unfamiliar with one or the other of thesesubjects. It is shown that information theory provides valuable concepts forthe experimental use of ion traps, especially error correction, and converselythe ion trap provides a valuable link between information theory and physics,with attendant physical insights. Example parameters are given for the case ofcalcium ions. Passive stabilisation will allow about 200 computing operationson 10 ions; with error correction this can be greatly extended.Comment: This is an invited contribution for Applied Physics B. It will be  submitted at the end of September (1996), and I would greatly appreciate any  constructive criticism or suggested additions before then (email  a.steane@physics.ox.ac.uk). 37 pages plus 8 figures. Replaced version  corrects figure reference

The ion trap quantum information processor