The Board of Trustees of the American Mathematical Society, expressing its belief that a great deal of time would be saved for mathematicians if they could study a textbook of Russian precisely adapted to their needs, granted to the present author nine months leave of absence from his duties as Editor of Translations. To the Board, and to Gordon L. Walker, the Exec­ utive Director of the Society, who took the initiative in this matter with his customary energy and good will, the author is deeply gratefUl for the opportunity to write such a book. For indispensable help and advice in the preparation of the book, which was written chiefly in Gottingen, Moscow and Belgrade, gratitude is due to many people, especially to Martin Kneser of the Mathematics Institute in Gottingen, S. M. Nikol'skii and L. D. Kudrjavcev of the Steklov Institute in Moscow, T. P. Andjelic of the Mathematics Institute in the Yugoslav Academy of Arts and Sciences, G. Kurepa and B. Terzic of the Mathematics and Slav­ istics Departments in the University of Belgrade, and Alexander Schenker of the Department of Slavic Languages and Literatures in Yale University. For expert assistance, both secretarial and linguistic, the author is indebted to his wife Katherine and his son William, for proficient typing of the Reading Selections to Tamara Burmeister, Secretary of the Slavistics Depart­ ment in Belgrade, and Christine Lefian, editorial assistant in the American Mathematical Society. Providence, USA S. H.

1 Plan of the book.- 2 Inheritance, transliteration and loan-translation.- 3 Roots and prefixes.- 4 The Indo-European language and its descendants.- 5 Vowel gradation.- 6 Consonant variation.- 7 The alphabet.- I Alphabet.- 1 The Cyrillic alphabet.- 2 Memorizing the alphabet.- 3 History of the Cyrillic consonants.- 4 The vowel-symbols; the basic vowel-scheme.- 5 Hard and soft consonants.- 6 The spelling rule.- II Pronunciation.- 1 Importance of pronunciation.- 2 The six Russian vowel-sounds.- 3 Monosyllables for practice in pronunciation.- 4 Remarks on hard and soft consonants.- 5 Hard and soft consonants in English and Russian.- 6 A first approximation to Russian pronunciation.- 7 The letter ? when pronounced but not written.- 8 The "separating" hard and soft signs.- 9 The letter ? when written.- 10 Assimilation of voiced and voiceless consonants.- 11 Consonant clusters.- 12 Words of more than one syllable; accents.- III Inflection.- 1 The concept of declension.- 2 The three declensions.- 3 Frequency of occurrence of nouns of the eight types.- 4 Declension in the plural.- 5 Remarks on the exercises.- 6 The concept of grammatical gender.- 7 Declension of pronouns.- 8 Declension of adjectives.- 9 The numerals.- 10 Adjective-noun phrases; italics.- 11 Comparative and superlative of adjectives and adverbs.- 12 The uninflected parts of speech.- 13 The verb; present imperfective and future perfective.- 14 The future imperfective and the past tense.- 15 The adjectival and adverbial participles.- IV Aspect.- 1 Difference in meaning between the two aspects.- 2 Aspect regarded as a correspondence.- 3 Perfective partners and lexical compounds.- 4 The imperfectivizing suffixes.- 5 Table of aspectual and lexical compounds of verbs.- 6 Notes on the table.- V Vocabulary.- 1 Planof the chapter.- 2 The three "verbs of motion".- 3 The root ?ep- (?-) take.- 4 The roots ?a?- lay and c?a- stand.- 5 Verbs formed from adjectives.- 6 Twenty roots of considerable productivity.- 7 Forty roots of moderate productivity.- 8 Other nouns and adjectives.- Readings.- Preliminary remarks.- Section A Extracts from elementary analytic geometry and calculus.- A1 Distance between points.- A2 Division of a segment.- A3 Polar coordinates.- A4 Parallel translation of axes.- A5 Rotation of axes.- A6 Equations of the straight line.- A7 The line through a point in a given direction.- A8 Normal equation of the line.- A9 General linear equation of the line.- A10 The line through two given points.- A11 Segments on the axis (i.e. intercepts).- A12 Definition of a vector.- A13 Sum of vectors.- A14 Scalar products.- A15 General equation of the plane.- A16 Parametric equations of a line in space.- A17 Introduction of irrational numbers.- A18 Continuity of the domain of real numbers.- A19 Least upper and greatest lower bounds.- A20 Fundamental theorem on real numbers.- A21 The elementary functions.- A22 Limit of a function.- A23 Continuity of a function.- A24 Heine-Borel and Weierstrass theorems.- A25 Derivative of a function.- A26 Equation of the tangent to a curve.- A27 Maximum and minimum of a function.- A28 Differentiation of a sum, difference, product.- A29 Derivative of a composite function.- A30 Indefinite integral.- A31 Integration by change of variable.- A32 Integration by parts.- A33 Fundamental theorem of the integral calculus.- Section B Extracts from elementary algebra and analysis.- B1 Operations on sets.- B2 Properties of the operations on sets.- B3 One-to-one correspondence.- B4 Equivalent sets.- B5 Ordered sets.- B6 Similar sets.- B7 Algebraicoperations.- B8 Rings.- B9 Examples of rings.- B10 The zero of a ring.- B11 Domains of integrity.- B12 Fields.- B13 Unit element.- B14 Division.- B15 Characteristic of a field; prime fields.- B16 Isomorphism.- B17 Ordered rings.- B18 Properties of ordered rings.- B19 Axiom of Archimedes.- B20 The natural numbers.- B21 Addition and multiplication of natural numbers.- B22 Order of the natural numbers.- B23 Subtraction and division of natural numbers.- B24 Fundamental theorem of arithmetic.- B25 The extension principle.- B26 Performability of operations in an extension.- B27 Equivalence classes.- B28 The ring of integers up to isomorphism.- B29 The ring of integers.- B30 The field of rational numbers.- B31 Quotient fields.- B32 The field of real numbers.- B33 The field of complex numbers.- Section C More advanced topics.- Cl Functions of a real variable.- C2 Functions of several complex variables.- C3 Summability theory of divergent series.- C4 Generalized functions.- C5 Calculus of variations.- C6 Theory of groups and generalizations.- C7 Theory of numbers.- C8 Mathematical logic.- C9 Partial differential equations.- C10 Hilbert space.- C11 Differential geometry.- C12 Topology.- Name and Subject Index.