What is a good book to learn how to manipulate inequalities with absolute values?

The book The Cauchy-Schwarz Master Class by Steele is focused specifically on manipulating inequalities and contains detailed solutions to all of the exercises, making it a good choice for self-study. I, too, am lousy with inequalities and the (regrettably small) amount of time I have spent with this text has been profitable.

Here are some of the basics.

1. If $|a|\leq b$ (where $b\geq 0$) then $-b \leq a \leq b$
2. If $|a|\geq b$ (where $b\geq 0$) then either $a \geq b$ or $a\leq -b$
3. $|ab|=|a||b|$ and, as a consequence, $|a^n|=|a|^n$
4. the triangle inequality $|a+b| \leq |a| + |b|$
5. If $f(x)$ is monotone increasing, then if $x\leq y$ then $f(x)\leq f(y)$. See the wikipedia article on inequalities
6. Somewhat less used in undergrad calculus is the Cauchy Schwarz inequality $| x_1 y_1 + x_2 y_2|^2 \leq (x_1^2 + x_2^2 ) (y_1^2+y_2^2)$