The basis of this book was a special course given by the author at the Mechanics-Mathematics Faculty of Moscow University. The material presumes almost no previous knowledge and is completely understandable to a reader who is in command of a standard course of mathematical analysis. There are an extensive bibliography and indexes which will be helpful to students.

Table of Contents

• Normal algorithms and enumerable sets
• Constructive real numbers
• Constructive convergence. Effective uncountability of the constructive continuum
• The impossibility of certain algorithms connected with constructive real numbers
• Constructive functions
• Differentiation of constructive functions
• Riemann integration of constructive functions
• Singular coverings and some of their applications
• Constructive metric spaces