Chapter 1 Basic Techniques for Proving Inequalities Chapter 2 Identical Transformation of the Sum Chapter 3 Substitution Method Chapter 4 Proof by Contradiction Chapter 5 Construction Method Chapter 6 Local Inequality Chapter 7 Mathematical Induction and Inequality Chapter 8 Inequality and Extremum for Multi-Variable Function Chapter 9 Special Techniques for Proving Inequalities Detailed Solutions to Exercises