Abstract : This work is an expanded version of a set of lecture notes corresponding to a course given by the author during the period November 1978 to January 1979. Analytical methods for the solution of moving object search problems are developed from 'first principles.' This work complements the first author's CNA memorandum but otherwise there is little overlap with the existing literature on search theory. The approach taken is tutorial, in that the solutions of harder problems are motived by the solutions of simpler problems. There are exercises interspersed throughout the work; the solutions of some of these are given in the appendix. This work is concerned with mathematical analysis and not with modeling target motion or detection functions and not with the development of computer codes.