This study aid is based on many years’ experienceof lecturing on mathematical analysis at the firstcourse at the physics faculty of Moscow University. Itis intended for students as well as for teachers, especiallyyoung ones, who are starting their lecturing career.The hook covers the analysis of functions of one variable,including the concepts of Lebesgue measure andLebesgue integral. It is not a collection of problems inthe ordinary sense. As can be seen from its structure, itsaim is to help the student master the material both activelyand informally. As a rule, the material in each sectionis divided into four subsections.Translated from the Russian by Irene Aleksanova