The present volume of the series in Pure and Applied Mathe­ matics is devoted to two basic operations of mathematical analysis — differentiation and integration. It discusses the complex of problems directly connected with the operations of differentiation and integra­ tion of functions of one or several variables, in the classical sense, and also elementary generalizations of these operations. Further generalizations will be given in subsequent volumes of the series, volumes devoted to the theory of functions of real variables and to functional analysis.Together with an earlier volume in the series, volume 69, L. A. Lyusternik and A. R. Yanpol’skii, Mathematical Analysis (Functions, Limits, Series, Continued Fractions), the present one includes material for a course of mathematical analysis, which is treated in a logically connected manner, briefly and without proofs, but with many examples worked in detail.