This is a study aid presenting the methods of solving problems in algebra. It is based on the experience of teaching mathematics at the preparatory faculty of Moscow University.

The following four themes are considered in the book: Real Numbers and Algebraic Expressions, Equations, Inequalities and Systems, Elements of Combinatorics, and Complex Numbers.

Each section begins with a concise theoretical introduction, and then worked problems illustrate the methods of solution. In order to show the typical methods, the solutions given are not always the shortest. Sometimes several ways of solving the same problem are given to compare the efficiency of the methods. Each section ends with assignments which will help the student to master the concepts and methods of problem solving.

Both the number of problems in an assignment and the number of the assignments themselves considerably exceed the minimum necessary for mastering the material and we do not think that all the problems and all the solution methods will be studied with the same thoroughness. The main purpose of the book is to give a possible scheme for studying a theme and to substantiate it with selected material and appropriate instructions, thus ensuring a sufficiently large choice of problems for mastering the concepts and methods.

The book will help high-school students revise the theory they studied at school and recollect the techniques and methods of problem solving.

We are grateful to Professor M.K.Potapov, who reviewed the book and made some useful remarks.