This SIAM Classics edition is an unabridged, corrected republication of the work first published in 1977. It provides a compendium of applied aspects of ordering and selection procedures and includes tables that permit the practitioner to carry out the experiment and draw statistically justified conclusions. These tables are not readily available in other texts. Although more than 1000 papers and several books on the general theory of ranking and selection have been published since this book first appeared, the methodology is presented in a more elementary fashion, with numerous examples to help the reader apply it to a specific problem. There is a dichotomy in modern statistics that distinguishes between analyses done before an experiment is completed and those done afterward. Ranking and selection methods are useful in both of these categories. The authors provide an alternative to the overused "testing the null hypothesis" when what the practitioner really needs is a method of ranking k given populations, selecting the t best populations, or some similar goal. That need and purpose is as important today as when the subject was first developed nearly 50 years ago.