The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities - Steele, J. Michael (MAA problem books series., 2004)
Using the Cauchy-Schwarz inequality as the initial guide, this text explains the concepts of mathematical inequalities by presenting a sequence of problems as they might have been discovered, the solutions to which can either be found with one of history's great mathematicians or by the reader themselves.