The preface says: This little book is intended primarily for high school pupils, teachers of mathematics and students in teachers training colleges majoring in physics or mathematics. It deals with various applications of the method of mathematical induction to solving geometric problems and was intended by the authors as a natural continuation of I. S. Sominsky’s booklet  The Method of Mathematical Induction published (in English) by Mir Publishers in1975. Our book contains 38 worked examples and 45 problems accompanied by brief hints. Various aspects of the method of mathematical induction are treated in them in a most instructive way. Some of the examples and problems may be of independent interest as well. The book was translated from the Russian by Leonid Levant and was first published by Mir in 1979. This was also published in the Topics in Mathematics series in 1963, and was translated by A.W. Goodman and Olga A. Titelbaum.Introduction: The Method of Mathematical Induction 7 Sec. 1. Calculation by Induction 12 Sec. 2. Proof by Induction 20 Map Colouring 33 Sec. 3. Construction by Induction 63 Sec. 4. Finding Loci by Induction 73 Sec. 5. Definition by Induction 80 Sec. 6. Induction on the Number of Dimensions 98 1. Calculation bv Induction on the Number of Dimensions 106 2. Proof by Induction on the Number of Dimensions 109 3. Finding Loci by Induction on the Number of Dimensions 126 4. Definition by Induction on the Number of Dimensions 130 References 132