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By algebraic inequalities I mean inequalities like Cauchy's inequality, the AM-GM inequality etc. I need it for the International Mathematics Olympiad (IMO), so I hope I can find some books that introduce inequalities on that level. While I can only find problems on websites like M.SE. or AoPS (most of which are almost unintelligible to me), I want a book that provides a detailed, reader-friendly approach to that subject. Any recommendations? Thanks in advance.

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The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele.

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Basics of Olympiad Inequalities (Samin Riasat)

www.aam.org.in/site/st_material/14.pdf

It's a free pdf document and it is very useful.

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  • $\begingroup$ Thank you. That's true. I'm currently reading this note. One flaw is just that it doesn't provide complete answers to the exercises, and I don't consider the questions to be "basic". Then M.SE. turns out to be quite useful since I can ask questions here. :) $\endgroup$
    – Yuxiao Xie
    Commented Apr 17, 2016 at 6:31
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$1$. Garling - Inequalities

$2$. Cvetkovski - Inequalities

$3$. Zawaira - A Primer for Mathematics Competitions

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Old and New Inequalities Volume 1 - Titu Andreescu

Old and New Inequalities Volume 2 - Vo Quoc Ba Can et.al.

Algebraic Inequalities - Vasile Cirtoaje

Secrets in Inequalities - Pham Kim Hung [Volume 1 and 2]

Inequalities with Beautiful Solutions - Vo Quoc Ba Can et.al.

To my best knowledge, all the problems presented in the above mentioned books are solved.

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  • $\begingroup$ Do you have old and new inequalities volume 2 $\endgroup$
    – user690488
    Commented Mar 15, 2020 at 18:44
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B.J.Venkatachala for inequality is a very good book for what you are searching.You may see this book.

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With the note that certain algebraic inequalities require some calculus to derive and/or grasp the full context:

$1$ Hardy, Littlewood, Polya - Inequalities;

$2$ Beckenbach, Bellman - Inequalities.

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