This textbook on mathematical analysis is based on many years’ experience of lecturing at a higher technical college. Its aim is to train the students in active approach to mathematical exercises, as is done at a seminar. Much attention is given to problems improving the theoretical background. Therefore standard computational exercises are supplemented by examples and problems explaining the  theory, promoting its deeper understanding and stimulating precise  mathematical thinking. Some counter examples explaining the need for  certain conditions in the formulation of basic theorems are also  included. The book is designed along the following lines. Each section opens with a concise theoretical introduction containing the principal definitions, theorems and formulas. Then follows a detailed solution of one or more typical problems. Finally, problems without solution are given, which are similar to those solved but contain certain peculiarities. Some of them are provided with hints. These sections should prove of interest to the inquiring student, and possibly also to lecturers in selecting material for classwork or seminars. This book was translated from the Russian by Leonid Levant. The book was published by first Mir Publishers in 1973.