This manual is intended for mathematicians who are fairly well acquainted with Russian and have a need to translate mathematical materials into English. Both of the editors worked extensively with such translations and, in the process of their work, kept records of problems, both grammatical and stylistic, that commonly turned up. The main part of the booklet presents typical examples: first the Russian text is given, then the faulty translation, an acceptable translation, and usually some comments. Although such a manual cannot be exhaustive, it does deal with many common mistakes and misconceptions. The examples are taken from the mathematical literature, making the manual of particular interest to mathematicians; however, it should also be useful to physicists, chemists, engineers, and anyone else concerned with the translation of scientific Russian into English.