Throughout the preparation of each edition of this dictionary, the guiding objective has been to make it useful for students, scientists, engineers, and others interested in the meaning of mathemati cal terms and concepts. It is intended to be essentially complete in the coverage of topics that occur in precollege or undergraduate college mathematics courses, as well as covering many topics from beginning graduate-level courses. In addition, many other interesting and important mathematical concepts are included. When preparing this edition, emphasis was given on revising and updating topics included in previous editions and to introducing many new topics, so as to reflect recent interesting and exciting developments in mathematics. An important feature continued and extended in this edition is the multilingual index in French, German, Russian, and Spanish. The English equivalents of mathemati cal terms in these languages enable the reader not only to learn the English meaning of a foreign-language mathematical term, but also to find its definition in the body of this book. Although this is by no means a mere word dictionary, neither is it an encyclopedia. It is a correlated condensation of mathematical concepts, designed for time-saving reference work. Never theless, the general reader can come to an understanding of a new concept by looking up unfamiliar terms in the definition at hand and following this procedure down to familiar concepts.