109 Inequalities
From the AwesomeMath Summer Program

This book is probably one of the best books to learn about inequalities. I enjoyed this book because of four reasons:

(1) The book assumes little prior knowledge about inequalities -- it starts from the very basics, teaching you everything you need to know.

(2) This book goes into a lot of depth into the theory behind inequalities. It explores the basic inequalities such as the Trivial, AM-GM, and Cauchy Schwarz inequalities, as well as the lesser known inequalities such as Nesbitt's Inequality and the Rearrangement Inequality.

(3) The authors go beyond just explaining the theorems and their proofs. They also sometimes include generalizations for the theorems. For example, the Nesbitt's inequality chapter includes 3 generalizations and one refinement of the original inequality.

(4) Lastly, the authors include several problems and applications of the inequalities presented in the book. These are particularly useful since they demonstrate the versatility of the results discussed in the book. They also enhance the understanding of the theorems to the point where we can apply them to other problems we encounter somewhere else.

In "109 Inequalities", Mr. Andreescu goes in depth, teaching us the fundamental inequalities that make up common Olympiad Inequalities. Knowing only the inequality won't help, so Mr. Andreescu not only gives us a rigorous definition (and proof), but gives us tricks and tactics on how to deal with hard inequality problems,from just multiplying it with another polynomial to using more than one inequality to solve a problem. This book has helped me gain an arsenal of tactics to deal with when faced with an USA(J)MO, ISL, virtually any olympiad problem involving Inequalities. I would highly recommend this book for any IMO aspirants.