本书是基于作者在新加坡教授15年的数学竞赛课程讲义发展而来的，它的内容和深度超过了普通教学大纲，并且引入了大量现代数学的概念与方法。本书是这套讲义初中卷的第一卷，分成15讲。每一讲的核心部分是概念、理论与解题方法，书中提供了大量的示例来解释和丰富主题内容，并展示它们的应用。书中也提供了很多习题供读者自己练习，并配有习题解答。其中，书中的示例与习题很多都来源于真实的中国、俄罗斯、美国和新加坡的数学竟赛考题。

Preface
Acknowledgments
Abbreviations and Notations
1 Operations on Rational Numbers
2 Monomials and Polynomials
3 Linear Equations of Single Variable
4 System of Simultaneous Linear Equations
5 Multiplication Formulae
6 Some Methods of Factorization
7 Absolute Value and Its Applications
8 Linear Equations with Absolute Values
9 Sides and Angles of a Triangle
10 Pythagoras' Theorem and Its Applications
11 Congruence of Triangles
12 Applications of Midpoint Theorems
13 Similarity of Triangles
14 Areas of Triangles and Applications of Area
15 Divisions of Polynomials
Solutions to Testing Questions
Index