A beautiful part in Maths is inequality. There are a lot of techniques and theorems related to inequality. This is the main reason that inequality problems appear in most Mathematics Competitions. Therefore, if you want to be a part of the competitions, mastering in inequality is one thing that you must do.

Challenging Problems in Inequalities is a little book about inequalities. This book will provide you with the basics, techniques and theorems in inequalities. We will guide you through many interesting things in inequalities. This book was written in three main parts. The first part is about techniques and theorems in proving inequalities. The second part is about problems. And the last part of the book is about solutions.

In the first part of the book, we try to dive readers into the basic inequalities. We lead readers to understand many well-known theorems such as QM-AM-GM-HM inequality, Cauchy-Schwarz inequality, rearrangement inequality, Jensen's inequality, Schur's inequality and etc. Moreover, in each chapter, we give many examples in order to make to make sure that readers understand well about the theorem. Readers should keep in mind that learning maths is not about memorizing but it is all about understanding. The more you understand about the lesson, the more you perform really well in solving problems.

In the second part of the book, we listed many challenging problems from around the world. The aim of this part is to help readers to practice their understanding in the first part. Readers should try their best to solve the given problems before seeing the solutions. It is good to figure the answers out by yourself. However, do not worry if you cannot solve them since the last part of the book is about solutions. In this part, we provide readers very detailed solutions to each problems. All problems were solved step by step. This part will help readers to evolve a lot. We hope this book will help readers a lot in inequalities.