本书对初三奥数竞赛中的问题加以甄选和整理，并加以讲解。另一方面通过讲解，帮助学生更好地理解其中蕴含的理论和思路。本书按照初三年级区分，结合初一教材，将课堂知识与奥林匹克数学竟赛相结台，强化基础，拔高难度，注重培养学生的学科兴趣和探索能力。

葛军，博士，中国数学奥林匹克高级教练，南京师范大学兼职教授、江苏省中学数学教学研究会副理事长、南京师大附中校长。主要从事竞赛数学、解题理论、数学课程与教学论、网络课程、学校教育等方面的研究，已发表论文70余篇，参编教材与著作30多部，其中主编《新编奥林匹克数学竞赛指导（高中）》、《小学数学奥林匹克启蒙》，编著《初等数学研究教程》、《数学教学论与数学教学改革》等。

Preface
1.Quadratic Equations
2.Equations that can be Transformed into Quadratic Equations
3.Discriminant of Quadratic Equation
4.Relationship Between Roots and Coefficients and Application
5.Simultaneous Quadratic Equations with Two Unknowns
6.Integer Roots of Quadratic Equation
7.Perfect Square Numbers
8.Quadratic Functions
9.Quadratic Inequalities
10.Distribution of Roots of Quadratic Equation
11.Maximum and Minimum Values of Quadratic Functions
12.Maximum and Minimum Values of Simple Fractional Functions
13.Trigonometric Functions of Acute Angle
14.Solving Right Triangles
15.Rotations
16.Basic Properties of Circles
17.Positional Relation Between Line and Circle
18.Positional Relation of Two Circles
19.Power of A Point Theorem
20.Four Concyclic Points
21.Problems of Geometric Fixed Value
22.Five Centers of Triangle
23.Geometric Inequalities
24.Indefinite Equations
25.Reductio ad Absurdum
26.Extreme Principle
27.Coloring Problems
28.Probability
Solutions
1.Quadratic Equations
2.Equations that can be Transformed into Quadratic Equations
3.Discriminant of Quadratic Equation
4.Relationship Between Roots and Coefficients and Application
5.Simultaneous Quadratic Equations with Two Unknowns
6.Integer Roots of Quadratic Equation
7.Perfect Square Numbers
8.Quadratic Functions
9.Quadratic Inequalities
10.Distribution of Roots of Quadratic Equation
11.Maximum and Minimum Values of Quadratic Functions
12.Maximum and Minimum Values of Simple Fractional Functions
13.Trigonometric Functions of Acute Angle
14.Solving Right Triangles
15.Rotations
16.Basic Properties of Circles
17.Positional Relation Between Line and Circle
18.Positional Relation of Two Circles
19.Power of A Point Theorem
20.Four Concyclic Points
21.Problems of Geometric Fixed Value
22.Five Centers of A Triangle
23.Geometric Inequalities
24.Indefinite Equations
25.Reductio ad Absurdum
26.Extreme Principle
27.Coloring Problems
28.Probability