In general the theory of random walks raises challenging questions for anyone who has more than a passing interest in understanding the be-havior of stock prices. Unfortunately, however, most discussions of the theory have appeared in technical academic journals and in a form which the non-mathematician would usually find incom-prehensible. This article describes, briefly and sim-ply, the theory of random walks and some of the important issues it raises concerning the work of market analysts. To preserve brevity some aspects of the theory and its implications are omitted.More complete (and also more technical) discus-sions of the theory of random walks are available elsewhere; hopefully the introduction provided here will encourage the reader to examine one of the more rigorous and lengthy works listed at the end of this article.