The present problem book is meant for high-school studentswho intend to enter technical colleges. I t contains more thantwo thousand problems and examples covering all divisionsof high-school mathematics.The main aim of the book is to help students to revise theirschool knowledge of mathematics and develop a techniquein solving a variety of problems.The book consists of nine chapters divided into sections,each of which deals with a certain theme. The problems ona definite theme are arranged in the order of increasingdifficulty, which makes it possible for a student to graduallyacquire the necessary techniques and experience in problemsolving. Thus, the problems are classified as far as possible.Most of the problems were given at the entrance examinationsin various colleges to the USSR in recent years. All theproblems are supplied with answers, and some of them withsolutions or instructions. The words "Solution" and "Hint"are replaced by the signs A and. respectively. The list ofdesignations makes the use of the book more convenient.All the contributors to the book have a long experienceas lecturers at preparatory courses of colleges, as teachersat high schools specializing in physics and mathematics andas examiners in mathematics.This book was translated from the Russian by I. A. Aleksanova. Thebook was published by first Mir Publishers in 1985.