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Предлагаемая книга посвящена рассмотрению основных проблем математического анализа. Одной из ее отличительных черт является особое внимание, уделяемое аксиоме выбора. Книга состоит из двух частей - развитие основ математического анализа до аксиомы выбора и после неё. Первая часть включает следующие разделы: теория вещественных чисел, числовые последовательности и ряды, многочлены, предел функции, непрерывность и дифференцируемость. Вторая часть начинается с формулировки и систематического использования аксиомы выбора. Основные разделы второй части: теоремы о непрерывных и дифференцируемых функциях, неопределённые, определённые и несобственные интегралы. Ещё одна особенность книги - строгость изложения материала. Практически все сформулированные утверждения доказаны.
Книга ориентирована на самый широкий круг читателей, поскольку базой для её понимания является школьный курс математики. Материал может быть полезен учащимся физико-математических школ, студентам университетов с расширенной математической подготовкой, а также может использоваться в системе дополнительного образования.
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