While all human languages are likely to be genetically related, the remoter relationships cannot be demonstrated by reliable linguistic methods because the languages in question have diverged too much. Any demonstration of a relationship between languages depends on finding words & grammatical affixes of systematically similar shape & roughly equivalent meaning in the languages in question. This book addresses the practical aspects of the problem of chance resemblances; only elementary probability theory is needed to address the problem. The author discusses strictly limited, tightly controlled types of similarity between words, because those are easiest to understand & analyze; then he discusses more complex cases. Illustrations.